Arithmetic, algebra, number theory, sequence and series, analysis, ...
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Post by yogeshspat » Wed Nov 27, 2013 5:40 am

Require solution to this problem.

I want to sum the terms in following progressive manner,

Can you give the ultimate equation by which i can calculate the result of this equation for n=1, 2,3,4,5,6, etc.

x+(x-y)+(x-y-y)+(x-y-y-y)+(x-y-y-y-y)+........n times

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Re: Mathematics

Post by nicolas.patrois » Wed Nov 27, 2013 1:30 pm

Easy for x, and for y, consider 1+2+3+4+…

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Re: Mathematics

Post by TheEvil » Thu Nov 28, 2013 7:00 am

First of all, it is not an equation. But if you are intrested in the closed form of that series:

x*n - n*(n-1)*y/2

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Re: Mathematics

Post by SNaveenMathew » Sun May 11, 2014 7:16 pm

Let us define the mth term of this sequence:
tm = x-y-y-y-...(m times) = x-y(1+1+1+1+...(m times)) = x-my
Sn = Sum(m=1 to n){tm}
= Sum(m=1 to n){x-my}
= Sum(m=1 to n){x} - Sum(m=1 to n){my}
= x*Sum(m=1 to n){1} - y*Sum(m=1 to n){m} as x and y are constant over all values of m
= x*n - [frac]y*n*(n+1),2[/frac]

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