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February 23rd, 2017, 06:26 PM  #1 
Newbie Joined: Feb 2017 From: Denmark Posts: 12 Thanks: 1  Techniques for adding the numbers from n to n
Hey guys, I have some homework which I can't figure out how to do. The question is simple: Find a formula that can find the sum of A to B while adding 1 to A in a specific amount of times. Like adding 1 to A and adding that ontop of the previous A in n times. To give you an idea of what I mean, it's basically the same as going into Excel, adding 1, 2, 3, 4 and so on in a column like A, then marking all of those numbers and getting the sum of it. What would the formula for that be? Picture: https://gyazo.com/1a25ae38cc1b9270e1a2d1db271611ca The numbers on the left Y axis = amount of times The numbers on the right side "1, 2, 3, 4" is A + 1 The SUM = A + 1 * amount of times. So basically, does anyone know the formula that excel uses to the "autosum" function? Last edited by emilo0212; February 23rd, 2017 at 07:00 PM. Reason: wrong question 
February 23rd, 2017, 06:33 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,500 Thanks: 757 
$\displaystyle{\sum_{k=m}^n}~k = $ $\displaystyle{\sum_{k=0}^{nm}}~(k+m) = $ $\displaystyle{\sum_{k=0}^{nm}}~k+\displaystyle{\sum_{k=0}^{nm}}~m = $ $\dfrac{(nm)(nm+1)}{2} + m(nm+1)=$ $(nm+1)\left(\dfrac{nm}{2} + m\right) =$ $(nm+1)\left(\dfrac{n+m}{2}\right)$ 
February 23rd, 2017, 06:34 PM  #3  
Newbie Joined: Feb 2017 From: Denmark Posts: 12 Thanks: 1  Quote:
 
February 23rd, 2017, 06:43 PM  #4 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,500 Thanks: 757  
February 23rd, 2017, 06:44 PM  #5 
Newbie Joined: Feb 2017 From: Denmark Posts: 12 Thanks: 1  
February 23rd, 2017, 06:51 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,053 Thanks: 1395 
To ensure we understand your requirement correctly, can you give a simple numerical example, complete with all the calculated results?

February 23rd, 2017, 06:52 PM  #7 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,500 Thanks: 757  
February 23rd, 2017, 06:53 PM  #8  
Newbie Joined: Feb 2017 From: Denmark Posts: 12 Thanks: 1  Quote:
https://gyazo.com/1a25ae38cc1b9270e1a2d1db271611ca  
February 23rd, 2017, 06:54 PM  #9 
Newbie Joined: Feb 2017 From: Denmark Posts: 12 Thanks: 1  Ahh, okay, well I'll try that out, although I dont think that's the case since I probably explained the question in a wrong way. I'll update my question now with a picture, so you can compare & understand.

February 23rd, 2017, 07:10 PM  #10 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,500 Thanks: 757 
$A + (A+1) + (A+2) \dots + (B1) + B = $ $\displaystyle{\sum_{k=A}^B}~k = (BA+1)\left(\dfrac{A+B}{2}\right)$ 

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