- published: 21 Nov 2013
- views: 73037
Sum may refer to:
As an acronym, SUM may refer to:
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, and so forth. A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, the term number may refer to a symbol, a word, or a mathematical abstraction.
In mathematics, the notion of number has been extended over the centuries to include 0, negative numbers, rational numbers such as and , real numbers such as and , complex numbers, which extend the real numbers by including , and sometimes additional objects. Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of the natural numbers.
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15 … is an arithmetic progression with common difference of 2.
If the initial term of an arithmetic progression is and the common difference of successive members is d, then the nth term of the sequence () is given by:
and in general
A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.
The behavior of the arithmetic progression depends on the common difference d. If the common difference is:
Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 + 14 = 16). Thus 16 × 5 = 80 is twice the sum.
The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + · · · is a divergent series. The nth partial sum of the series is the triangular number
which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting results, some of which have applications in other fields such as complex analysis, quantum field theory, and string theory. Many summation methods are used in mathematics to assign numerical values even to a divergent series. In particular, the methods of zeta function regularization and Ramanujan summation assign the series a value of −1/12, which is expressed by a famous formula:
In a monograph on moonshine theory, Terry Gannon calls this equation "one of the most remarkable formulae in science".
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country"). In common language, words used for counting are "cardinal numbers" and words used for ordering are "ordinal numbers".
Some authors begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, …, whereas others start with 1, corresponding to the positive integers 1, 2, 3, …. Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, but in other writings, that term is used instead for the integers (including negative integers).
The natural numbers are the basis from which many other number sets may be built by extension: the integers, by including an additive inverse (-n) for each natural number n (and zero, if it is not there already, as its own additive inverse); the rational numbers, by including a multiplicative inverse (1/n) for each integer number n; the real numbers by including with the rationals the (converging) Cauchy sequences of rationals; the complex numbers, by including with the real numbers the unresolved square root of minus one; and so on. These chains of extensions make the natural numbers canonically embedded (identified) in the other number systems.
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
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 ...
The video describes how to easily find out sum of first n natural numbers within seconds. More videos👇 Simplification 👉https://youtu.be/qKST4migPxo Multiplication tricks 👉https://youtu.be/-emYt7Ve0SM Addition & Substraction Tricks 👉https://youtu.be/MW_UvQ9wD0A BODMAS Rules👉https://youtu.be/0dT0UquNqWo Facebook page 👉https://www.facebook.com/SmartStudyForCareer/
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...
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.
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.
In this video explained about easy way for sum of “ n” consecutive number of natural, even, odd and square of natural, even and odd and also cube of natural, even and odd. This YouTube " Siva Math Tips" channel provided videos regarding easy mathematics calculations, mathematical reasoning, reasoning for competitive exams, math magic tricks, math magic, vedic maths tricks, math for kids, fast calculations in mathematics, This channel very much helpful to all students and elders to improving the creative thinking skills, brain storming, Fast calculation and mental health. Google Plus: https://plus.google.com/+sivaalluri Twitter: https://twitter.com/Sivamaths4u Facebook: https://www.facebook.com/alluri.sivaramakrishna Linked In : https://www.linkedin.com/in/siva-rama-krishna-alluri-10373...
Explains how to find the sum of numbers
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...
The video describes how to sum up first n odd numbers in an easy way.
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...
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 ...
A little trick to sum Fibonacci numbers. Try it out.
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...
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. Sum of Natural number tricks👉https://youtu.be/UTJgdohUegk Sum of Odd numbers tricks👉https://youtu.be/Y_QV_3JXVSI Simplification👉https://youtu.be/s4D0XjPrzVM Follow me on Facebook👉https://www.facebook.com/SmartStudyForCareer/
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c program to find sum of n numbers (summation) using for loop write a program to find sum of n numbers using loop write a program to add n numbers using loop write a program to get summation of n numbers write a program to demonstrate usage of for loop write a program to calculate summation of n numbers write a program for summation in c language write a c program to find sum of n numbers write a c program to calculate summation how to find summation of n numbers in c language using for loop and while loop. how does for loop work in c language. what is the difference between for loop and while loop. what is the difference between while loop and do while loop.
This is a description and tutorial about how to use the Apple iWork Numbers Sum function. To use the SUM function and all functions, just select any cell and click the equal '=' key. Then add the SUM function. So, if you wanted to get the Sum of cell A1 and B1 the function would be =SUM(A1:B1).
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
More free lessons at: http://www.khanacademy.org/video?v=i7iKLZQ-vCk
----------------------------------------------------------------------------------------------------- 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. ------------------...
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. Follow me on Facebook👉https://www.facebook.com/SmartStudyForCareer/ Google+👉 https://plus.google.com/111082316974868239587 Twitter👉https://mobile.twitter.com/ss_career
This video contains all information about how to find out sum of natural numbers in C Language with all programming tricks and traps with complete solution.
2688 GOD SUM OF DIVISORS FOR 2017 GOD 26 ELOHIM 62 JESUS IN GREEK 88 ELOHIM IN HEBREW 86 ALL THESE NUMBER FOUND IN SUM OF DIVISORS FOR 2017 2688. IN SPHENIC NUMBERS GOD APPEARS 2017 IS SPHENIC NUMBER Number 2017 is a composite number. Factors of 2017 are 5 * 13 * 31. Number 2017 has 8 divisors: 1, 5, 13, 31, 65, 155, 403, 2017. Sum of. How to find the number of divisors of a given composite number with derivation/ justification.
Guys this video is meant to clear students basic c programming ..How to write a program.. I hope this Video will help you. Please share this video so that everyone can understand the basic of C programming language.PEACE OUT😊😊
he sum of two numbers is 23. When seven times the smaller number is subtracted from three times the larger number, the result is -1. What is the larger of the two numbers?
How to perform multiplication of number having same tens and their ones sum is 10 within a second . this video is made to make easiness in mathematical calculations without calculator and written solution. for further detail watch this video. our mission is to make study easy for all . because eduactiion is not only for rich people but is same for poor as well but rich people get admissions in high fee school to get quality of education and poor can not afford it so we got a new way to deliver quality of education via internet because we have to-pest teachers in almost all fields. for more stay connected .... with us
In this class, we'll study about 'Estimating the sum or difference of numbers'. If you've any doubts or topics you want us to cover, please write it in the comments section. Download Toppr App: Andriod Play Store: http://bit.ly/2jTmjef iOS App Store: http://apple.co/2A8pIdz Download Doubts on Chat App: Andriod Play Store:http://bit.ly/2B6w7oy iOS App Store: http://apple.co/2ziAA75 About Toppr: Toppr is an after school learning app for K12 students. Our vision is to personalise education using technology. We cater to the curricular learning needs of students who are preparing for various school board exams, olympiads and scholarship tests as well as for engineering and medical college entrance exams. The award winning Toppr platform leverages 4 methods of learning, each delivering a ta...
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http://demonstrations.wolfram.com/SumOfNumbersOnInvisibleFaces The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. The faces of a polyhedron are labeled 1, 2, 3, .... Find the sum of the numbers on the invisible faces. Contributed by: Izidor Hafner Audio created with WolframTones: http://tones.wolfram.com
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...
----------------------------------------------------------------------------------------------------- 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. ------------------...
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In this video I go over the proof of the summation of n positive integers which are raised to the power of 4. The proof although straight forward is very tedious and requires a lot of algebra. Download the notes in my video: https://www.dropbox.com/s/xhoeh1l6xkbqoq1/416%20-%20Sum%20of%20n%20integers%20to%20the%20power%20of%204.pdf Related Videos: Sigma Notation - A brief Introduction: http://youtu.be/Gew7y73NY30 Sum of "n" Consecutive Integers - Simple Proof : http://youtu.be/tpkzn2e5mtI Sum of the squares of "n" Consecutive integers - Simple Proof: http://youtu.be/TeF09H13qyI Sum of the Cubes of "n" Consecutive integers - Simple Proof : http://youtu.be/drguFeiCMZw Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ Types of Numbers: Natural, Integers, R...
This video is contributed by Sandeep Please Like, Comment and Share the Video among your friends and family members. Also, Subscribe if you haven't already! :) For any query or suggestion mail me at my email id:- sandeep2006iiitm@gmail.com Follow me on Facebook:- https://www.facebook.com/Sandeep02aug Like our Facebook page:- https://www.facebook.com/bsiacademy16 Follow us on Twitter:- https://twitter.com/bsiacademy Follow us on Google+:- https://plus.google.com/u/0/111901664357973607756
أ.محمود سعدون _ماث _الصف الثالث الابتدائي_الترم الأول__المنهج المصري _الوحدة الثالثة الدرس الأول - Finding sum of 2 numbers - نوفمبر 2017م. تابع جداول مواعيد الحلقات ع صفحتنا ع فيسبوك https://www.facebook.com/elschoola/ وده فهرس الاسكوله اللي فيه كل المواد بتاعتنا https://goo.gl/8Ex6dc
A story of pi, prime numbers, and complex numbers, and how number theory braids them together. Check out Remix careers: https://www.remix.com/jobs The fact that only primes that are one above a multiple of four can be expressed as the sum of two squares is known as "Fermat's theorem on sums of two squares": https://goo.gl/EdhaN2 Special thanks to the following patrons: http://3b1b.co/leibniz-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various s...
How a certain perspective on what the Riemann zeta function looks like can motivate what it might mean beyond its domain of convergence. One month free audible trial, I recommend "The Art of Learning": https://www.audible.com/3blue1brown Support on patreon, and get early access to future "Essence of" series: https://www.patreon.com/3blue1brown There are posters for this visualization of the zeta function at http://3b1b.co/store Music by Vince Rubinetti: https://soundcloud.com/vincerubinetti/riemann-zeta-function Check out some of Vince's other work here: http://www.vincentrubinetti.com/ For those who want to learn more about complex exponentiation, here are a few resources: - My video on the topic: http://youtu.be/mvmuCPvRoWQ - Mathologer's: https://youtu.be/-dhHrg-KbJ0 - Better Expl...
Confused 1+2+3+…=-1/12 comments originating from that infamous Numberphile video keep flooding the comment sections of my and other math YouTubers videos. And so I think it’s time to have another serious go at setting the record straight by having a really close look at the bizarre calculation at the center of the Numberphile video, to state clearly what is wrong with it, how to fix it, and how to reconnect it to the genuine math that the Numberphile professors had in mind originally. This is my second attempt at doing this topic justice. This video is partly in response to feedback that I got on my first video. What a lot of you were interested in were more details about the analytic continuation business and the strange Numberphile/Ramanujan calculations. Responding to these requests, ...
This trigonometry video tutorial explains how to use the sum and difference identities / formulas to evaluate sine, cosine, and tangent functions that have angles that are not commonly found in the unit circle. Examples include angles both in degrees and radians.
Create Sum two NumbersApp using eclipse by Jasbir
Question discussion of Career Point, Bansal/Vibrant Q 1. Sum of all the numbers greater than 10,000 formed by the digits 1,3,5,7,9 no digits being repeated. Q 2. Sum of all the numbers greater than 10,000 formed by 0,2,4,6,8 no digit being repeated. Q 3. Sum of all the distinct 4 digits number contain only the digits 1,2,3,4,5 each at most once is given by. Q 4. No of 7 digits integers with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only is JEE-09 Q 5. No of 7 digits number if sum of their digits is 1)63 2) 62 3)61 4)60 Subscribe, like and Drop your mail id to get a gift in your inbox :) For any online study support or for any kind of study material drop a mail to gyanunplugged@gmail.com Stay tuned and Have a great life.