# How does this image prove the identity $1+2+3+4\cdots + (n-1) = \binom{n}{2}$? [duplicate]

Possible Duplicate:
Proof for formula for sum of sequence 1+2+3+…+n?

Proof without words:

$\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad$

How does this image prove the identity $1+2+3+4\cdots + (n-1) = \binom{n}{2}$?

I found this here; could anybody explain this in a lucid manner?

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Is it ironic that the post is titled "Proof without words"? ;) –  Srivatsan Oct 28 '11 at 23:38