Expanding the product of a series

Hello everyone,

I hope this advanced enough to be in this section.

I am doing a math project, and at the moment I am confronted with this expression:

∏_(y=1)^(n-1) 2 (a^(1/n) sin(yπ/n)) [capital pi y=1 -> n-1]

I know from Wolfram|Alpha (see link) that this is equal to:

n*a^((n-1)/n).

However I want to be able to show this manually, and I have no idea of how to approach the task at hand.

Can someone please explain the steps involved to get to the answer above?

Thank you very much.

Re: Expanding the product of a series

I found this page on PlanetMath that uses Euler's formula.

Re: Expanding the product of a series

Wow thank you, emakarov.

Very convenient. The derivation is surprisingly close to what I am doing, but more concise.

And to think they give us this in high school...

Re: Expanding the product of a series

Quote:

Originally Posted by

**ImaginaryMe** And to think they give us this in high school...

http://i3.kym-cdn.com/photos/images/...ib3wo1_400.jpg.