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.