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prove that:

[tex]\forall n \in N \forall 0<=k<=2^{n-1} (C(2^n,k)=\sum_{j=0}^{k}C(2^{n-1},j)C(2^{n-1},k-j))[/tex]

attempt at solution

induction seems to be too long im opting for a shorter solution, so the sum that it's wrriten in the rhs is the square of the sum of the term C(2^(n-1),j) but other than that don't know how to procceed.

any advice?

thanks in advance.

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# Homework Help: Binomial identity.

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