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Math Help - exponential?

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    1

    Exclamation exponential?

    ive been sent this problem and am a little stuck:

    r = 1 - sum_(k=0)^infinity((-1)^k theta^(1+2k))/(1+2k)!

    there was no multiplier put between the k and the theta, i'm guessing this was just a typo? so it would look like this:

    r = 1 - sum_(k=0)^infinity((-1)^k*theta^(1+2k))/(1+2k)!

    the sum_(k=0)^infinity(theta^(1+2k))/(1+2k)! looks like an exponential. is this right, even though the term is 1+2k? could it then be written as:

    r = 1 - e^theta*(-1)^k ??

    three variables now, i'm confused. my math is very rusty.

    any help or guidance would be great

    thank!
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Hi

    \sum_{k=0}^{\infty} \frac{(-1)^k \:\theta^{2k+1}}{(2k+1)!} = \sin \theta

    You can find this relation starting from

    e^x = \sum_{k=0}^{\infty} \frac{x^k}{k!} and \sin x = \frac{e^{ix}-e^{-ix}}{2i}
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