I want to prove

So, simply what I chose to do is to first prove

by (mathematical) induction, and then use the same method for

The first works out fine, no problem there at all.

The second part causes problems.

I manage to show P(x) true for x=1 (wow, I am realy amazing)

And then I make my claim:

I then do my calculations and I get:

Witch is not right.

Anyone know or have a clue about where I am off?

Is there another part of my calculations that I should include? Please say so if that is the case, I try to include just the parts where I think I am wrong (everything only if I have no clue).