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Math Help - Evaluating series

  1. #1
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    Evaluating series

    i need help evaluating this:  \sum_{n=0}^\infty \frac{1}{2}^n {e^{-jw(n+1)}} i know the answer is:  {e^{-jw}}\frac{1}{1 - \frac{1}{2}e^{-jw}} however, im not quite sure how to get to it. I can kind of see how I could evaluate it, but is there a more general way to solve these?
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  2. #2
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    Quote Originally Posted by p00ndawg View Post
    i need help evaluating this:  \sum_{n=0}^\infty \frac{1}{2}^n {e^{-jw(n+1)}} i know the answer is:  {e^{-jw}}\frac{1}{1 - \frac{1}{2}e^{-jw}} however, im not quite sure how to get to it. I can kind of see how I could evaluate it, but is there a more general way to solve these?
    You can re-arrange it into  e^{-jw} \sum_{n=0}^\infty \left( \frac{e^{-jw}}{2}\right)^n and then use the formula for the sum of an infinite geometric series.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    You can re-arrange it into  e^{-jw} \sum_{n=0}^\infty \left( \frac{e^{-jw}}{2}\right)^n and then use the formula for the sum of an infinite geometric series.
    ahh i see it now. Thanks.
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