I am trying to figure out how to show that when n is a positive integer.

My Work

P(n) is for

Basis step - P(1) is true because

Inductive step - Assume is true,

then is true

Then prove , but I can't figure out how to get this P(k+1) equation to equal

I received the reply below, which is probably a wonderful answer, but I am unclear as to where in the 3rd line came from. I though you had to add the initial part of the P(k+1) equation, which is , to both sides of the P(k) equation as I did above.

First Reply

Assume for n.

We want to show that

,<--- negative of the induction hypothesis

by the induction hypothesis.

So, is true.