Hi all!

I'm new here and I could use some help on a homework question.

Problem

Given the following recursive definition:

I have to proof, using induction, that

My current proof is as follows:

Proof

Base step

The formula is correct for the cases n=0 and n=1 (Can be easily verified).

Induction step

Assume the formula is correct for n, we can fill this in:

However, I think I am missing some important induction steps. I don't see the connection between the base step and the induction step.

Any help is appreciated, thanks in advance!