15 Aug 2011

Prove this identity

A note to future me:

Today you were trying to do probability questions with your pathetically sad probability skills and you found that
Dare you to prove it.

Your arrogant younger self.

Here's a hint:
Why? Can you think of a combinatorial interpretation for this? Proving it through algebra is trivial. Thinking of an interpretation may lead to some actual learning.

From the identity above, you also managed to find that it implies: \[\sum _{i=0}^n \binom{t-i}{m}=\binom{t+1}{m+1}-\binom{t-n}{m+1}.\] Prove this identity.

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