I need to prove that G_(2^n) <= A_(2^n) by using induction on n.

G_n = geometric mean and A_n is arithmetic mean.

I have a hint which says let m be such that 2^m >= n and set a_(n+1) = a_(n+2) = ... = a_(2^m) = A_n

I don't have idea how to apply this hint on this problem.

Please help me out...