Notice on my last step (the nasty looking one) if you replace n by n+1 on the right, you get the expression on the left. That's what is going to let the series telescope. Each term cancels out the one before it. Sort of like this #1 + 1/2 - 1/2 + 1/3 - 1/3 + 1/4 - 1/4...# etc. Each term cancels the one before it, in this case leaving only the first.
Can some one help me?