I really can't remember (if I have ever known this): which series is this and how to demonstrate its solution?∑i=1ni=n(n+1)2

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I really can&#039;t remember (if I have ever known this): which series is this and how to demonstrate its solution?∑i=1ni=n(n+1)2

Anzante2m · Accepted Answer

Write out this sum twice, once is direct order, and once in reverse:  1+2+…+(n−1)+n=s  n+(n−1)+…+2+1=s  Now add up column-wise:  (n+1)+(n+1)+…+(n+1)+(n+1)=2s  There are exactly n terms here (as many as the number of terms in the sum). Hence:  n(n+1)=2s  Now solve for s.

Jonathan Burroughs · Accepted Answer

This is an Arithmetic Series starting from 1 with difference 1.  ∑i=1ni=1+2+3+4+…+n=n(n+1)2

karton · Accepted Answer

This is not a series. This sum is named Gauss sum and that formula n(n+1)2 you can prove it using induction. The exercise starts from the following sum: 1+2+...+100 and the way you can classify the terms of this sum. 1+2+...+100=(1+100)+(2+99)+...(50+51)

I really can't remember (if I have ever known this):

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