Please no double posting. On typing math symbols, see this thread for more: LaTex Tutorial

You can see the code that generates the image by clicking on it.

As for your problem, let's look at the inductive step.Assumingthat , our goal is to prove that .

Looking at the LHS, notice that:

Now I highlighted the part in red for a reason .. and it shouldn't be too hard to show that this is bigger than .