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 Subject: Excel Formula Question Category: Computers > Algorithms Asked by: boschdog-ga List Price: \$20.00 Posted: 27 Jun 2006 19:21 PDT Expires: 27 Jul 2006 19:21 PDT Question ID: 741617
 ```I am trying to create a "simple" formula in an excel cell that reads any number, ex. the number 8, and computes the following =(+1+2+3+4+5+6+7+8)with the result being 36 or number 31 =(+1+2+3+4+5+6+7+8...+31)with the formula result of 496. I am not looking for a formula that just sums up the logical series of a sequential list of numbers, i.e. =sum(A1:A31) with cell A1 being 1 , A2 being 2, and so on.```
 Subject: Re: Excel Formula Question Answered By: tox-ga on 27 Jun 2006 20:10 PDT
 ```Hi there boschedog-ga, What you are looking for is the formula for an arithmetic series (an arithmetic series is the sum of an arithmetic sequence). We call a sequence of numbers an arithmetic sequence if the difference of any two consecutive term is the same. An example is a sequence of odd or even numbers, in which case the common difference is 2, or the sequence of natural numbers which you listed in your question, in which case the difference is 1. Now let's get right to the point. Assuming that you have a number, eg 8, in cell A1, the formula for the sum would be: =A1*(A1+1)/2 There are a few ways to understand why this is so. First method: Assume that the number you have is "n". So, you're looking for 1 + 2 + 3 +...+ (n-2) + (n-1) + n. Let's call this sum, "S". Write out the sequence again below it, but in reverse order and add them. S = 1 + 2 + 3 + ... + (n-2) + (n-1) + n S = n + (n-1) + (n-2) + ... + 3 + 2 + 1 -------------------------------------------------------------- S+S = (n+1) + (n+1) + (n+1) + ... + (n+1) + (n+1) + (n+1) Now, we can see that the left side is equal to 2S since we just added the same series to itself. On the right side, you see that every pair of terms add up to (n+1). We also know that there are n pairs of (n+1) since S has n terms. Thus 2S = (n+1)*n S = n(n+1)/2 Second method: If you want to see a graphical interpretation of the sum, please check out this link: http://merganser.math.gvsu.edu/calculus/summation/arithmetic.html I hope this has helped and please feel free to ask for any clarification and I'd be happy to help you further. The formula for different arithmetic series (where the difference between the terms isn't 1) requires slight adjustment but can be derived in the same way - please let me know if you require the general formula. Cheers, Tox-ga```
 `N*(N+1)/2`
 ```N*(N+1)/2 this```
 ```=(A1*(A1+1))/2 paste this in cell A3 put value in A1 that u need like if no is 5 put in A1 u will get value in A3 **** a beginner can understand beginner well**** :) :) :) :) :)```