• Sum of first n natural numbers - Derivation of a formula

    Derivation of the formula in a way which is easy to understand. It will also help student to remember the formula easily. This is the foundation for next few videos on Arithmetic progression. This will also help u in solving mental ability problems asked in various competitive exams. This Method of addition is also useful in finding the sum of various Number patterns and Puzzles. For more such videos visit or Subscribe to my You Tube Channel https://www.youtube.com/MathsSmart For collaborations and business inquiries, please contact via Channel Pages: http://ChannelPages.com/MathsSmart

    published: 21 Nov 2013
  • ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

    Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help More links & stuff in full description below ↓↓↓ EXTRA ARTICLE BY TONY: http://bit.ly/TonyResponse The sum of all natural numbers (from 1 to infinity) produces an "astounding" result. ANOTHER PROOF & EXTRA FOOTAGE: http://youtu.be/E-d9mgo8FGk MORE: http://youtu.be/0Oazb7IWzbA NY Times article on this: http://nyti.ms/1iftqSv Tony Padilla and Ed Copeland are physicists at the University of Nottingham. They talk physics at our sixty symbols channel: http://www.youtube.com/sixtysymbols Grandi's Series: 1-1+1-1.... http://www.youtube.com/watch?v=PCu_BNNI5x4 Read more about divergent series: http://en.wikipedia.org/wiki/Divergent_series We also here that Chapter XIII of Konrad Knopp's book, "Theory and ...

    published: 09 Jan 2014
  • Finding the Sum of numbers

    Explains how to find the sum of numbers

    published: 09 Mar 2010
  • How to Find the Sum of odd Numbers - Using Sum of N terms Formula of Arithmetic Series

    http://ItsMyAcademy.com/arithmetic-sequences/ For Free Complete Video Tutorial on Sequence & Series. For more videos on sequence and series. To Find the sum of odd numbers we have to first make an arithmetic sequence or arithmetic series then we can easily find the sum of odd numbers from sum of n term formula of arithmetic sequence. its is simple . In this video we are dealing with such problems. Here we need to find the sum of odd numbers from 0 to50 using the sum of n term formula of arithmetic sequence. To do so we will first arrange the all odd numbers between 0 to 50 in increasing order then taking 1 as first term and 49 as last term we will make an arithmetic series. By using nth term formula of arithmetic sequence we will get the total number of terms of the sequence and then by ...

    published: 25 Jan 2011
  • Sum of Fibonacci Numbers Trick

    A little trick to sum Fibonacci numbers. Try it out.

    published: 18 Sep 2016
  • Excel Tutorial 1 of 25 - How to Add in Excel - SUM Formula

    Microsoft Excel Tutorial 1 of 25. How to total numbers in Excel using the SUM function and autosum feature. How to add separated groups of numbers together. How to use the SUM formula in Excel.

    published: 26 Jan 2013
  • Sum of two numbers Word Problem

    published: 05 Nov 2012
  • How To Sum The Numbers 1 to 100 - If Math Was A Sport Historical Fiction

    It's the final play of the 1787 World Math Championships. The talented 10-year old Gauss faces a challenging question from his math teacher. Will the young student show up his teacher, or does he still have lessons to learn? I wanted to explain how to sum the numbers from 1 to 100 in a fun and creative way. This dramatization is based on a true story. **Thanks To My $10+/mo Patreon Supporters** Kyle Sports sound effects CC BY 3.0 (https://creativecommons.org/licenses/by/3.0/us/) Modified from SoundBible.com http://soundbible.com/1882-Football-Crowd.html (GoGo) http://soundbible.com/1834-End-Of-Game.html (Mike Koenig) http://soundbible.com/1881-Sports-Crowd.html (GoGo) Some Details About The Story Gauss sum 1 to 100 stories (the legends) http://bit-player.org/wp-content/extras/gaussfil...

    published: 03 Apr 2015
  • Apple iWork Numbers Sum Function

    This is a description and tutorial about how to use the Apple iWork Numbers Sum function.

    published: 12 May 2015
  • Sum of Natural Numbers (second proof and extra footage)

    MAIN VIDEO IS AT: http://youtu.be/w-I6XTVZXww More links & stuff in full description below ↓↓↓ Ed Copeland and Tony Padilla are physicists at the University of Nottingham. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://te...

    published: 11 Jan 2015
  • The sum of all counting numbers equals WHAT?

    This is the second half of a lesson, watch the first half here: http://youtu.be/yudhkUUzAgY This is a well-known and hugely controversial result. The "proof" I've demonstrated is not the only way to show it - there are far more sophisticated and convincing ways to do it - but suffice to say that I went through it to raise questions and provoke thought rather than to make a statement about its validity or otherwise! Hope it makes you think.

    published: 17 Jul 2014
  • Response to Numberphile's ASTOUNDING 1+2+3+4+... = minus 1/12 (sum of natural numbers to infinity)

    This is a response to the Numberphile video that claims 1+2+3+4+... = -1/12. We explain the flaws, and tell you the real meaning of -1/12 in this context. Several methods return this -1/12 result. Obviously no method can add up infinitely many non-zero terms, and so what they do is produce is a limit value. This limit value is merely the limit of the area between the x-axis and the partial sum formula (from x = -1 to 0). Just as -1/12 is supposedly the sum of all natural numbers, the 'sum of the squares of natural numbers' (and indeed any even power) is supposedly zero, and the 'sum of the cubes of the natural numbers' is supposedly equal to or related to 1/120. Again these values are the simply the limit of the area of the respective partial sum expressions between -1 and 0. If we plot...

    published: 26 Oct 2015
  • Sum of "n" Consecutive Integers - Simple Proof

    In this video I go through Karl Gauss's ingenious proof for the formula of a sum of the first n positive and consecutive integers. Gauss derived this when he was only 10 years old!! Download the notes in my video: https://www.dropbox.com/s/u305wrxmt4r1lzl/203%20-%20Proof%20of%20Sum%20of%20n%20positive%20integers.pdf Related Videos: Sigma Notation - A brief Introduction: http://youtu.be/Gew7y73NY30 Types of Numbers: Natural, Integers, Rational, Irrational, and Real Numbers: http://youtu.be/U22Z1q_Ibqg . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab...

    published: 12 Oct 2012
  • Sum of the squares of "n" Consecutive integers - Simple Proof

    In this video I show the proof for determing the formula for the sum of the squares of "n" consecutive integers, i.e. 1^2 + 2^2 + 3^2 +.... + n^2. This is a pretty abstract proof and makes use of the useful "telescoping" or collapsing sum which I illustrate in the video. The formula for the sum of squares comes up very often in calculus so it's a good idea to understand the proof! Download the notes in my video: https://www.dropbox.com/s/rgv3obty1w3p9k2/204%20-%20Proof%20of%20sum%20of%20n%20squares.pdf Related Videos: Sigma Notation - A brief Introduction: http://youtu.be/Gew7y73NY30 Sum of "n" Consecutive Integers - Simple Proof : http://youtu.be/tpkzn2e5mtI Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ Types of Numbers: Natural, Integers, Ration...

    published: 14 Oct 2012
  • 4.1. Sum of Numbers - Java

    ----------------------------------------------------------------------------------------------------- Starting out with Java: From control structures through objects Chapter 4 Programming Challenges -------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Sum of numbers Write a program that asks the user for a positive nonzero integer value. The program should use a loop to get the sum of all the integers from 1 up to the number entered. For example, if the user enters 50, the loop will find the sum of 1, 2, 3, 4, . . . 50. Gaddis, Tony (2015-05-29). Starting Out with Java: From Control Structures through Objects (Page 262). Pearson Education. Kindle Edition. ------------------...

    published: 01 Oct 2016
  • Art of Problem Solving: Sum the Numbers from 1 to 100

    Art of Problem Solving's Richard Rusczyk adds the numbers from 1 to 100... the fast way. Visit www.artofproblemsolving.com to learn more.

    published: 22 Dec 2011
  • Trick 35 Sum of First n Odd Numbers

    The video describes how to sum up first n odd numbers in an easy way.

    published: 09 Dec 2011
  • Sum of Rational and Irrational Numbers

    Will the sum of a rational and an irrational number be a rational number? Or will it be an irrational number? Or could it be either? To know more about Rational, Irrational and Real Numbers, please visit https://DontMemorise.com . Don’t Memorise brings learning to life through its captivating FREE educational videos. New videos every week. To stay updated, subscribe to our YouTube channel : http://bit.ly/DontMemoriseYouTube Register on our website to gain access to all videos and quizzes: http://bit.ly/DontMemoriseRegister Subscribe to our Newsletter: http://bit.ly/DontMemoriseNewsLetter Join us on Facebook: http://bit.ly/DontMemoriseFacebook Follow us : http://bit.ly/DontMemoriseBlog

    published: 19 Dec 2014
  • Program to Calculate Sum of Digits of a Given Number in C (HINDI)

    Subscribe : http://bit.ly/XvMMy1 Website : http://www.easytuts4you.com FB : https://www.facebook.com/easytuts4youcom

    published: 04 May 2014
  • sum of consecutive numbers problem using equation

    Learn to write equation for sum of consecutive numbers. The sum of three consecutive numbers is 225. find the numbers. To learn more such math lessons visit our channel youtube.com/MathsSmart or subscribe to http://www.youtube.com/MathsSmart.

    published: 01 Sep 2013
  • If sum of two consecutive numbers are 121, what are the numbers?

    published: 24 Mar 2015
  • Trick 34: Sum of first n even natural numbers

    The video describes how to easily find out sum of first n even natural numbers within seconds

    published: 08 Dec 2011
  • Learn programming now 27 ( While loop: Sum of numbers C++)

    In this video,. I use the While loop for finding the sum of set of integers. Let me know if you have any questions.

    published: 26 Jan 2011
  • Sum of Fibonacci numbers

    Coursera: http://www.coursera.org/learn/fibonacci Bookboon: http://bookboon.com/en/fibonacci-numbers-and-the-golden-ratio-ebook How to compute the sum over the first n Fibonacci numbers.

    published: 11 Oct 2016
  • Sum of numbers(in Hindi)

    published: 13 Sep 2017
  • Math trick sum of numbers

    published: 18 Oct 2016
  • Summing Consecutive Numbers

    published: 29 Nov 2014
  • Sum of number in C# .Net

    Sum of number in C# .Net

    published: 08 Oct 2016
  • Sum Numbers

    published: 29 Jul 2016
developed with YouTube
Sum of first n natural numbers - Derivation of a formula

Sum of first n natural numbers - Derivation of a formula

  • Order:
  • Duration: 8:11
  • Updated: 21 Nov 2013
  • views: 51784
videos
Derivation of the formula in a way which is easy to understand. It will also help student to remember the formula easily. This is the foundation for next few videos on Arithmetic progression. This will also help u in solving mental ability problems asked in various competitive exams. This Method of addition is also useful in finding the sum of various Number patterns and Puzzles. For more such videos visit or Subscribe to my You Tube Channel https://www.youtube.com/MathsSmart For collaborations and business inquiries, please contact via Channel Pages: http://ChannelPages.com/MathsSmart
https://wn.com/Sum_Of_First_N_Natural_Numbers_Derivation_Of_A_Formula
ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

  • Order:
  • Duration: 7:50
  • Updated: 09 Jan 2014
  • views: 5633392
videos
Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help More links & stuff in full description below ↓↓↓ EXTRA ARTICLE BY TONY: http://bit.ly/TonyResponse The sum of all natural numbers (from 1 to infinity) produces an "astounding" result. ANOTHER PROOF & EXTRA FOOTAGE: http://youtu.be/E-d9mgo8FGk MORE: http://youtu.be/0Oazb7IWzbA NY Times article on this: http://nyti.ms/1iftqSv Tony Padilla and Ed Copeland are physicists at the University of Nottingham. They talk physics at our sixty symbols channel: http://www.youtube.com/sixtysymbols Grandi's Series: 1-1+1-1.... http://www.youtube.com/watch?v=PCu_BNNI5x4 Read more about divergent series: http://en.wikipedia.org/wiki/Divergent_series We also here that Chapter XIII of Konrad Knopp's book, "Theory and Application of Infinite Sequences and Series", is very good if you can get your hands on it. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile
https://wn.com/Astounding_1_2_3_4_5_..._1_12
Finding the Sum of numbers

Finding the Sum of numbers

  • Order:
  • Duration: 3:22
  • Updated: 09 Mar 2010
  • views: 5043
videos
Explains how to find the sum of numbers
https://wn.com/Finding_The_Sum_Of_Numbers
How to Find the Sum of odd Numbers - Using Sum of N terms Formula of Arithmetic Series

How to Find the Sum of odd Numbers - Using Sum of N terms Formula of Arithmetic Series

  • Order:
  • Duration: 4:12
  • Updated: 25 Jan 2011
  • views: 63266
videos
http://ItsMyAcademy.com/arithmetic-sequences/ For Free Complete Video Tutorial on Sequence & Series. For more videos on sequence and series. To Find the sum of odd numbers we have to first make an arithmetic sequence or arithmetic series then we can easily find the sum of odd numbers from sum of n term formula of arithmetic sequence. its is simple . In this video we are dealing with such problems. Here we need to find the sum of odd numbers from 0 to50 using the sum of n term formula of arithmetic sequence. To do so we will first arrange the all odd numbers between 0 to 50 in increasing order then taking 1 as first term and 49 as last term we will make an arithmetic series. By using nth term formula of arithmetic sequence we will get the total number of terms of the sequence and then by simply using sum of n term of an arithmetic sequence we can easily calculate the sum of odd numbers. In this way we can get the sum of any odd numbers or even numbers from any where to any where. Just we should know the trick. Hope You learn how to find the sum of odd numbers using the n terms formula of arithmetic sequences. How to Find the Sum of odd Numbers - Using Sum of N terms Formula of Arithmetic Series In previous videos we learn to prove Arithmetic progression and then finding the sum. You are good in such problems too. Now friend in this video lesson we are learning to find the sum of odd numbers by the method of sequence and series specially applying the sum of arithmetic progression formula.. Well let's start how to find sum of odd numbers. I hope you always sit with pen and notebook. Great ! How you are feeling now! It was quite easy right just few steps to find the sum of odd numbers between any two numbers. Steps to find Sum of Odd Numbers 1. First write the first term and last term of odd number. The form it as a AP. 2. Apply the nth term formula of arithmetic progression on the last term. 3. By doing so (step2) we will get the value of total number of terms in that AP. 4. Now since we know first term(a), last term (l), number of terms (n), we can easily apply the sum of arithmetic progression formula to get the sum of odd numbers. Cheers! Well friend here I have listed few exercise related to sum of Arithmetic progression just like above. Please try to solve these all. It will really help you. Q1. Find the sum of all odd numbers between 100 to 200. (ans = 7500) Q2. Find the sum of all odd integers between 2 and 100 divisible by 3. (Ans = 867)
https://wn.com/How_To_Find_The_Sum_Of_Odd_Numbers_Using_Sum_Of_N_Terms_Formula_Of_Arithmetic_Series
Sum of Fibonacci Numbers Trick

Sum of Fibonacci Numbers Trick

  • Order:
  • Duration: 6:08
  • Updated: 18 Sep 2016
  • views: 207805
videos
A little trick to sum Fibonacci numbers. Try it out.
https://wn.com/Sum_Of_Fibonacci_Numbers_Trick
Excel Tutorial 1 of 25 - How to Add in Excel - SUM Formula

Excel Tutorial 1 of 25 - How to Add in Excel - SUM Formula

  • Order:
  • Duration: 3:29
  • Updated: 26 Jan 2013
  • views: 487986
videos
Microsoft Excel Tutorial 1 of 25. How to total numbers in Excel using the SUM function and autosum feature. How to add separated groups of numbers together. How to use the SUM formula in Excel.
https://wn.com/Excel_Tutorial_1_Of_25_How_To_Add_In_Excel_Sum_Formula
Sum of two numbers Word Problem

Sum of two numbers Word Problem

  • Order:
  • Duration: 2:39
  • Updated: 05 Nov 2012
  • views: 4726
videos
https://wn.com/Sum_Of_Two_Numbers_Word_Problem
How To Sum The Numbers 1 to 100 - If Math Was A Sport Historical Fiction

How To Sum The Numbers 1 to 100 - If Math Was A Sport Historical Fiction

  • Order:
  • Duration: 5:24
  • Updated: 03 Apr 2015
  • views: 37270
videos
It's the final play of the 1787 World Math Championships. The talented 10-year old Gauss faces a challenging question from his math teacher. Will the young student show up his teacher, or does he still have lessons to learn? I wanted to explain how to sum the numbers from 1 to 100 in a fun and creative way. This dramatization is based on a true story. **Thanks To My $10+/mo Patreon Supporters** Kyle Sports sound effects CC BY 3.0 (https://creativecommons.org/licenses/by/3.0/us/) Modified from SoundBible.com http://soundbible.com/1882-Football-Crowd.html (GoGo) http://soundbible.com/1834-End-Of-Game.html (Mike Koenig) http://soundbible.com/1881-Sports-Crowd.html (GoGo) Some Details About The Story Gauss sum 1 to 100 stories (the legends) http://bit-player.org/wp-content/extras/gaussfiles/gauss-snippets.html Normal distribution = Gaussian distribution http://en.wikipedia.org/wiki/Normal_distribution Euler vs Gauss is an argument http://forums.xkcd.com/viewtopic.php?f=17&t=35658 Gauss is known as the prince of mathematicians http://hsm.stackexchange.com/questions/284/how-did-gauss-become-the-the-prince-of-mathematicians If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter: http://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: http://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: http://www.patreon.com/mindyourdecisions Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) https://www.amazon.com/gp/product/1500497444 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1523231467/ "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. https://www.amazon.com/gp/product/1517421624/ "Math Puzzles Volume 2" is a sequel book with more great problems. https://www.amazon.com/gp/product/1517531624/ "Math Puzzles Volume 3" is the third in the series. https://www.amazon.com/gp/product/1517596351/ "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) https://www.amazon.com/gp/product/1517319307/ "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 3 reviews) https://www.amazon.com/gp/product/150779651X/ "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 1 review) https://www.amazon.com/gp/product/1500866148/
https://wn.com/How_To_Sum_The_Numbers_1_To_100_If_Math_Was_A_Sport_Historical_Fiction
Apple iWork Numbers Sum Function

Apple iWork Numbers Sum Function

  • Order:
  • Duration: 2:22
  • Updated: 12 May 2015
  • views: 6102
videos
This is a description and tutorial about how to use the Apple iWork Numbers Sum function.
https://wn.com/Apple_Iwork_Numbers_Sum_Function
Sum of Natural Numbers (second proof and extra footage)

Sum of Natural Numbers (second proof and extra footage)

  • Order:
  • Duration: 21:06
  • Updated: 11 Jan 2015
  • views: 1135816
videos
MAIN VIDEO IS AT: http://youtu.be/w-I6XTVZXww More links & stuff in full description below ↓↓↓ Ed Copeland and Tony Padilla are physicists at the University of Nottingham. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile
https://wn.com/Sum_Of_Natural_Numbers_(Second_Proof_And_Extra_Footage)
The sum of all counting numbers equals WHAT?

The sum of all counting numbers equals WHAT?

  • Order:
  • Duration: 8:52
  • Updated: 17 Jul 2014
  • views: 14464
videos
This is the second half of a lesson, watch the first half here: http://youtu.be/yudhkUUzAgY This is a well-known and hugely controversial result. The "proof" I've demonstrated is not the only way to show it - there are far more sophisticated and convincing ways to do it - but suffice to say that I went through it to raise questions and provoke thought rather than to make a statement about its validity or otherwise! Hope it makes you think.
https://wn.com/The_Sum_Of_All_Counting_Numbers_Equals_What
Response to Numberphile's ASTOUNDING 1+2+3+4+... = minus 1/12 (sum of natural numbers to infinity)

Response to Numberphile's ASTOUNDING 1+2+3+4+... = minus 1/12 (sum of natural numbers to infinity)

  • Order:
  • Duration: 6:37
  • Updated: 26 Oct 2015
  • views: 16840
videos
This is a response to the Numberphile video that claims 1+2+3+4+... = -1/12. We explain the flaws, and tell you the real meaning of -1/12 in this context. Several methods return this -1/12 result. Obviously no method can add up infinitely many non-zero terms, and so what they do is produce is a limit value. This limit value is merely the limit of the area between the x-axis and the partial sum formula (from x = -1 to 0). Just as -1/12 is supposedly the sum of all natural numbers, the 'sum of the squares of natural numbers' (and indeed any even power) is supposedly zero, and the 'sum of the cubes of the natural numbers' is supposedly equal to or related to 1/120. Again these values are the simply the limit of the area of the respective partial sum expressions between -1 and 0. If we plot the respective partial sum function, we see the increasing area under the curve in the positive direction (from x = 0) appears to be equal-and-opposite-to the increasing area under the curve in the negative direction (from x = -1). If we claim these areas cancel each other out, we are left with the area between -1 and 0. In the case of 1+2+3+4+..., the partial sum S = n(n+1)/2, and the limit of the area for the region between 0 and -1 is the definite integral of this function from -1 to zero, which is -1/12. Note that when we take a function that applies to positive whole numbers, and we plot it for decimal and negative values, the change from whole numbers to decimals often produces a region of length 1 to the left or right of the y-axis with symmetry around the line x = -0.5 or x = 0.5. However, if we said to ourselves "before we plot this function for negative values, let’s make it work for negative values just the same as it works for positive values" then we would no longer get results like -1/12. For example, if we wanted our partial sum expression n(n+1)/2 to work for the sum of negative whole numbers in the same way it works for positive whole numbers then we replace n by the modulus of n and multiply the whole thing by n/(modulus n), giving n(|n|+1)/2 This adjusted function does not produce the -1/12 area between 0 and -1 when plotted. In summary, this -1/12 result is simply one huge blunder. The mistake is one of taking a function that applies to just positive whole numbers, manipulating it in ways that bring fractions and negative numbers into play (such as by using division and subtraction operations), and then interpreting the result as though it still relates to positive whole numbers. There is nothing weird or mysterious going on, except for the delusion caused by the strong desire to have a way of adding up 'infinitely many' terms. This is very similar to the muddled argument of the so-called 'proof by geometric sum formula' that 0.999… equals 1. If we define 0.999… to be equal to the limit of the series 9/10 + 9/100 + … then we can find the limit of this series but we cannot 'prove' that 0.999… equals this limit; it is merely claimed to be true by definition (in which case proof is irrelevant because we only define things that cannot be proven). The geometric sum formula is a formula for finding the limit of a geometric series; it does not add up infinitely many terms. By calling this the 'geometric sum formula' instead of the 'limit of a geometric series formula' it creates the illusion that we have a formula for adding up infinitely many terms and thus this constitutes a 'proof ' for 0.999… = 1. There are no formulas or methods that can add up 'infinitely many' terms. The main flaw in the method that manipulates endless series (used in the Numberphile video) is that we must work with respect to the nth term in BOTH series. We cannot use n terms from one series and n+1 terms (or any number of terms) from another in order to make the trailing parts cancel out. You may ask why we can’t use the trailing parts in this flexible way. The answer is because it leads to contradictions. For example, if we start with S = 1 + 1 + 1 +…, then we can evaluate S – S to be any value we like by matching up the two series at different starting points. Placing S – S on both sides of an equals sign leads to 1=0, 1=2 or anything else you choose. Please do not include any links in your comments here, thank you. For more information about why the notion of 'infinity' should be removed from mathematics go to ExtremeFinitism.com.
https://wn.com/Response_To_Numberphile's_Astounding_1_2_3_4_..._Minus_1_12_(Sum_Of_Natural_Numbers_To_Infinity)
Sum of "n" Consecutive Integers - Simple Proof

Sum of "n" Consecutive Integers - Simple Proof

  • Order:
  • Duration: 4:03
  • Updated: 12 Oct 2012
  • views: 13865
videos
In this video I go through Karl Gauss's ingenious proof for the formula of a sum of the first n positive and consecutive integers. Gauss derived this when he was only 10 years old!! Download the notes in my video: https://www.dropbox.com/s/u305wrxmt4r1lzl/203%20-%20Proof%20of%20Sum%20of%20n%20positive%20integers.pdf Related Videos: Sigma Notation - A brief Introduction: http://youtu.be/Gew7y73NY30 Types of Numbers: Natural, Integers, Rational, Irrational, and Real Numbers: http://youtu.be/U22Z1q_Ibqg . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions Google Plus: https://mes.fm/gplus LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm Try our Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Try our Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps
https://wn.com/Sum_Of_N_Consecutive_Integers_Simple_Proof
Sum of the squares of "n" Consecutive integers - Simple Proof

Sum of the squares of "n" Consecutive integers - Simple Proof

  • Order:
  • Duration: 11:37
  • Updated: 14 Oct 2012
  • views: 97617
videos
In this video I show the proof for determing the formula for the sum of the squares of "n" consecutive integers, i.e. 1^2 + 2^2 + 3^2 +.... + n^2. This is a pretty abstract proof and makes use of the useful "telescoping" or collapsing sum which I illustrate in the video. The formula for the sum of squares comes up very often in calculus so it's a good idea to understand the proof! Download the notes in my video: https://www.dropbox.com/s/rgv3obty1w3p9k2/204%20-%20Proof%20of%20sum%20of%20n%20squares.pdf Related Videos: Sigma Notation - A brief Introduction: http://youtu.be/Gew7y73NY30 Sum of "n" Consecutive Integers - Simple Proof : http://youtu.be/tpkzn2e5mtI Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ Types of Numbers: Natural, Integers, Rational, Irrational, and Real Numbers: http://youtu.be/U22Z1q_Ibqg . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions Google Plus: https://mes.fm/gplus LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm Try our Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Try our Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps
https://wn.com/Sum_Of_The_Squares_Of_N_Consecutive_Integers_Simple_Proof
4.1. Sum of Numbers - Java

4.1. Sum of Numbers - Java

  • Order:
  • Duration: 20:42
  • Updated: 01 Oct 2016
  • views: 4831
videos
----------------------------------------------------------------------------------------------------- Starting out with Java: From control structures through objects Chapter 4 Programming Challenges -------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Sum of numbers Write a program that asks the user for a positive nonzero integer value. The program should use a loop to get the sum of all the integers from 1 up to the number entered. For example, if the user enters 50, the loop will find the sum of 1, 2, 3, 4, . . . 50. Gaddis, Tony (2015-05-29). Starting Out with Java: From Control Structures through Objects (Page 262). Pearson Education. Kindle Edition. -------------------------------------------------------------------------------------------------------------------------------------------------------------------- Bitcoin Address - 12uPbtoTBgxKG3ppxC2NSJYmmr5qipsbds Thanks :) --------------------------------------------------------------------------------------------------------------------------------------------------------------------
https://wn.com/4.1._Sum_Of_Numbers_Java
Art of Problem Solving: Sum the Numbers from 1 to 100

Art of Problem Solving: Sum the Numbers from 1 to 100

  • Order:
  • Duration: 2:49
  • Updated: 22 Dec 2011
  • views: 21656
videos
Art of Problem Solving's Richard Rusczyk adds the numbers from 1 to 100... the fast way. Visit www.artofproblemsolving.com to learn more.
https://wn.com/Art_Of_Problem_Solving_Sum_The_Numbers_From_1_To_100
Trick 35 Sum of First n Odd Numbers

Trick 35 Sum of First n Odd Numbers

  • Order:
  • Duration: 1:52
  • Updated: 09 Dec 2011
  • views: 10269
videos
The video describes how to sum up first n odd numbers in an easy way.
https://wn.com/Trick_35_Sum_Of_First_N_Odd_Numbers
Sum of Rational and Irrational Numbers

Sum of Rational and Irrational Numbers

  • Order:
  • Duration: 1:40
  • Updated: 19 Dec 2014
  • views: 2485
videos
Will the sum of a rational and an irrational number be a rational number? Or will it be an irrational number? Or could it be either? To know more about Rational, Irrational and Real Numbers, please visit https://DontMemorise.com . Don’t Memorise brings learning to life through its captivating FREE educational videos. New videos every week. To stay updated, subscribe to our YouTube channel : http://bit.ly/DontMemoriseYouTube Register on our website to gain access to all videos and quizzes: http://bit.ly/DontMemoriseRegister Subscribe to our Newsletter: http://bit.ly/DontMemoriseNewsLetter Join us on Facebook: http://bit.ly/DontMemoriseFacebook Follow us : http://bit.ly/DontMemoriseBlog
https://wn.com/Sum_Of_Rational_And_Irrational_Numbers
Program to Calculate Sum of Digits of a Given Number in C (HINDI)

Program to Calculate Sum of Digits of a Given Number in C (HINDI)

  • Order:
  • Duration: 12:32
  • Updated: 04 May 2014
  • views: 42867
videos
Subscribe : http://bit.ly/XvMMy1 Website : http://www.easytuts4you.com FB : https://www.facebook.com/easytuts4youcom
https://wn.com/Program_To_Calculate_Sum_Of_Digits_Of_A_Given_Number_In_C_(Hindi)
sum of consecutive numbers problem using equation

sum of consecutive numbers problem using equation

  • Order:
  • Duration: 6:33
  • Updated: 01 Sep 2013
  • views: 10289
videos
Learn to write equation for sum of consecutive numbers. The sum of three consecutive numbers is 225. find the numbers. To learn more such math lessons visit our channel youtube.com/MathsSmart or subscribe to http://www.youtube.com/MathsSmart.
https://wn.com/Sum_Of_Consecutive_Numbers_Problem_Using_Equation
If sum of two consecutive numbers are 121, what are the numbers?

If sum of two consecutive numbers are 121, what are the numbers?

  • Order:
  • Duration: 1:54
  • Updated: 24 Mar 2015
  • views: 1950
videos
https://wn.com/If_Sum_Of_Two_Consecutive_Numbers_Are_121,_What_Are_The_Numbers
Trick 34: Sum of first n even natural numbers

Trick 34: Sum of first n even natural numbers

  • Order:
  • Duration: 1:53
  • Updated: 08 Dec 2011
  • views: 19265
videos
The video describes how to easily find out sum of first n even natural numbers within seconds
https://wn.com/Trick_34_Sum_Of_First_N_Even_Natural_Numbers
Learn programming now 27 ( While loop: Sum of numbers C++)

Learn programming now 27 ( While loop: Sum of numbers C++)

  • Order:
  • Duration: 11:45
  • Updated: 26 Jan 2011
  • views: 23972
videos
In this video,. I use the While loop for finding the sum of set of integers. Let me know if you have any questions.
https://wn.com/Learn_Programming_Now_27_(_While_Loop_Sum_Of_Numbers_C_)
Sum of Fibonacci numbers

Sum of Fibonacci numbers

  • Order:
  • Duration: 8:44
  • Updated: 11 Oct 2016
  • views: 668
videos
Coursera: http://www.coursera.org/learn/fibonacci Bookboon: http://bookboon.com/en/fibonacci-numbers-and-the-golden-ratio-ebook How to compute the sum over the first n Fibonacci numbers.
https://wn.com/Sum_Of_Fibonacci_Numbers
Sum of numbers(in Hindi)

Sum of numbers(in Hindi)

  • Order:
  • Duration: 27:15
  • Updated: 13 Sep 2017
  • views: 4
videos
https://wn.com/Sum_Of_Numbers(In_Hindi)
Math trick sum of numbers

Math trick sum of numbers

  • Order:
  • Duration: 5:07
  • Updated: 18 Oct 2016
  • views: 3
videos
https://wn.com/Math_Trick_Sum_Of_Numbers
Summing Consecutive Numbers

Summing Consecutive Numbers

  • Order:
  • Duration: 1:36
  • Updated: 29 Nov 2014
  • views: 1537
videos
https://wn.com/Summing_Consecutive_Numbers
Sum of number in C#  .Net

Sum of number in C# .Net

  • Order:
  • Duration: 3:18
  • Updated: 08 Oct 2016
  • views: 11
videos
Sum of number in C# .Net
https://wn.com/Sum_Of_Number_In_C_.Net
Sum Numbers

Sum Numbers

  • Order:
  • Duration: 1:12
  • Updated: 29 Jul 2016
  • views: 0
videos
https://wn.com/Sum_Numbers
×