From looking at it, I think the best way would be to prove this by mathematical induction:

First, show that this is true for N=1:

But

, Thus

Now,

------------------------------------

Since we've shown this holds for N=1, Now we assume it holds for N=K

The hard [and really messy part] is to show it holds for N=k+1.

This means that

Note that

So

Knowing that

, we see that

We can further simplify

Since

Thus, we need to show that

Let's get the left side to look like the right side:

This completes the inductive step.

Does this make sense? Hopefully you can follow what I did...

--Chris

P.S. I wonder if anyone knows of a shorter way!?!?!?!