Use the binomial theorem (not induction) to prove: For all integers n >= 0,Sum_(i=0 to n) [(-1)^i * (n choose i) * 3^(n-i)] = 2^n.

Ok,so I worked my way downward for this problem,but all i have uptil now is

3^n [1 - n/3 + n(n-1)/(2!*3^2) + ......... + (-1)^n / 3 ^n]

idk how to further reduce this problem to make it equal to 2^n

Please help me on this one.

(Speechless)