# Thread: binomial theorem problem.

1. ## binomial theorem problem.

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.

2. $2^n = \left( {3 - 1} \right)^n = \sum\limits_{k=0}^{n} {{ n \choose k} \left( 3 \right)^{n - k} \left( { - 1} \right)^k }$