(Hmmm...It seems I was off by a term in my earlier post. Galactus has it right.)
Have you tried an induction proof?
For n = 1:
Since this is good. (The formula also works for .)
So it works for some n. Let's see if it works for n + 1.
Now,
By hypothesis so
should be true.
On the LHS:
=
=
=
Similarly we may show that the RHS becomes
Which again gives:
So the two sides are equal.
So the theorem is true for n and n + 1 etc.
-Dan