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,
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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!?!?!?!