I remember that quite some time ago, when I first saw this, I didn't believe it was true. Of course, trying for a few values made me see that it was probably true, so all that was left was proving it - now that's up to you

Prove that for all natural n, the following holds:

For those who don't like summation symbols, the above is just math language to say that:

Please don't reveal your answer yet, or post it 'covered'.