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Math Forum » Discussions » Math Topics » discretemath

Topic: Combinatorical Proof
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Petteri

Posts: 1
Registered: 5/21/10
Combinatorical Proof
Posted: May 21, 2010 5:22 PM
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Hi all!

I've been looking for solution for next problem:

How to prove:

\binom{n}{k}= 1 +
\sum_{j=0}^{k-1}\sum_{i=0}^{n-k-1}\binom{i+j}{j}


It is known as Pascal?s 3rd Identity. I have tried double induction for n and k, but have not succeeded.

Would make me very happy!

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