(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that for all positive integers n, the equality holds:

SUM(nCk)*2^k=(3^n+(-1)^n)/2

Note: The sum goes from k=0 to n. AND k has to be even.

2. Relevant equations

Binomial Theorem

3. The attempt at a solution

I know that if we use the binomial theorem for x=2 and y=1, we would get

(2+1)^n=SUM(nCk)*2^k , with no restriction for k being even. I wonder how to proceed.

Thanks.

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# Binomial Identity

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