Proving the Binomial Theorem: Simplifying 3^k C(n,k) = 2^2n

[jenny Downer]

Use the Binomial Theorem to show that n summation k-0 3^k C(n,k) = 2^2n

hint of the question is 3^k C(n,k) = 3^k 1^n-k C(n,k)

 

[Dick]

Think of applying the binomial theorem to the expansion of (1+3)^n.