Proof Involving Binomial Theorem

I have spent over 5 hours now trying to figure out how to prove this, and I still have got nothing. My teacher claims there is a somewhat simple way to prove this, and I cannot find it.

To see the thing that I am to prove, click this link : Yfrog - prooffm - Uploaded by Imageshack user

I am quite certain, but not entirely sure, that I have to use mathematical induction to prove it holds for n=0 and for n=n+1, but besides that, I am not sure how to go about things. I have tried everything I can think of.

If necessary, here is a link to the electronic version of our text book : http://math.sfsu.edu/beck/papers/aop.pdf . This problem is one from chapter #4. I feel like I should be able to use the Binomial Theorem somehow, but I cant get it.

Help would be appreciated great amounts! I must have this finished on monday.

Richard