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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 $ enter image description here

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"? ;)2011-10-28

1 Answers 1

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This shows that every yellow circle uniquely determines a pair of blue circles and vice versa. The number of yellow ones is the LHS, the number of pairs of blue ones is the RHS. Cute!

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    You should be able to figure out 4 (as in: 1)y=pb 2)y=lhs 3)pb=rhs imply 4)rhs=lhs).2011-10-28