# ali

## Proof for the summation formula S(n)=n*(n+1)/2

In Uncategorized on February 5, 2010 at 5:20 pm

I was explaining to a co-worker how supposed worked out the formula and illustrating my simple proof. I tried to look it up online, but didn’t find it.

So, here it is:

 1 2 … N = $\sum_{1}^{N}N$ N N-1 … 1 = $\sum_{1}^{N}N$ N+1 N+1 … N+1 = $N*(N+1)$

Thus

$\sum_{1}^{N}N + \sum_{1}^{N}N = N*(N+1)$
$2\sum_{1}^{N}N = N*(N+1)$
$\sum_{1}^{N}N = N*(N+1)/2$

For a better explanation, see this PDF.