What is the general method for finding the maximum values for N-Choose-K formulations?

In particular, my problem is asking for the k that makes (100-Choose-k)*2^k the maximum value.

I'm certain that the binomial theorem is required to tackle this problem, but the 2^k is throwing me off,

although I do know that, (100 choose 0)+(100 choose 1)+...+(100 choose 100) is 2^100.

Any help for me?