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Math Help - Expanding the product of a series

  1. #1
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    Exclamation 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.
    Last edited by ImaginaryMe; May 24th 2012 at 07:21 PM.
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  2. #2
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    Re: Expanding the product of a series

    I found this page on PlanetMath that uses Euler's formula.
    Thanks from ImaginaryMe
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  3. #3
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    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...
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  4. #4
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    Re: Expanding the product of a series

    Quote Originally Posted by ImaginaryMe View Post
    And to think they give us this in high school...
    .
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