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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.

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