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Math Help - [SOLVED] Geometric Series

  1. #1
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    Wink [SOLVED] Geometric Series

    K=0 to Infinity Where (-1)^K( X^2K+1). I cant figure out how to the get exponent on X to only be K


    Thanks 4 any help!
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  2. #2
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    Hello, nikie1o2!

    \sum^{\infty}_{k=0} (-1)^k x^{2k+1}

    I cant figure out how to the get exponent on x to only be k.
    . .
    I don't know what this means . . .
    In fact, you haven't told us what we're supposed to do . . .


    Write out the series: . S \;=\;x - x^3 + x^5 - x^7 + x^9 - \hdots

    We have a geometric series with first term a = x and common ratio r = -x^2

    If |r| < 1, the series will converge.

    And its sum will be: . S \;=\;\frac{x}{1+x^2}


    Is that any help?

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, nikie1o2!

    In fact, you haven't told us what we're supposed to do . . .


    Write out the series: . S \;=\;x - x^3 + x^5 - x^7 + x^9 - \hdots

    We have a geometric series with first term a = x and common ratio r = -x^2

    If |r| < 1, the series will converge.

    And its sum will be: . S \;=\;\frac{x}{1+x^2}


    Is that any help?
    Thats the correct answer in my textbook. thank you! I was thrown off because my professor said that "a" couldnt be a variable? I guess she was wrong
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