# Expanding the product of a series

• May 24th 2012, 06:14 PM
ImaginaryMe
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.
• May 25th 2012, 04:08 AM
emakarov
Re: Expanding the product of a series
• May 25th 2012, 10:13 AM
ImaginaryMe
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...
• May 25th 2012, 02:23 PM
emakarov
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.