The equation has a typo on the right hand side - it should be:
(note that the exponent in the numerator on the right hand side has 2^(n+1) in it, not 2^(r+1).
Using induction you first prove that this is true for n=1. Then show that if it's true for n=k it's also true for n = k+1.
Given: , then
which equals