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Math Help - Geometric Series Sum (Hoping somebody can check my work)

  1. #1
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    Geometric Series Sum (Hoping somebody can check my work)

    \sum_{n=0}^\infty \frac{2^{n}}{5^{2n+1}}

    I broke it up like {\frac{1}{5}}\sum_{n=0}^\infty ({\frac{2}{25}})^{n}

    I calculated the sum  S = \frac{1}{5}[\frac{\frac{1}{5}}{\frac{25}{25}-\frac{2}{25}}]

    Which ends up being  S = \frac{1}{23} ?
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    Re: Geometric Series Sum (Hoping somebody can check my work)

    Quote Originally Posted by AZach View Post
    \sum_{n=0}^\infty \frac{2^{n}}{5^{2n+1}}

    I broke it up like {\frac{1}{5}}\sum_{n=0}^\infty ({\frac{2}{25}})^{n}

    I calculated the sum  S = \frac{1}{5}[\frac{\frac{1}{5}}{\frac{25}{25}-\frac{2}{25}}]

    Which ends up being  S = \frac{1}{23} ?

    It should be
     S = \frac{1}{5}\left[\frac{1}{\frac{25}{25}-\frac{2}{25}}\right]

    Recall that S=\frac{a}{1-r} where a is the first term.
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    Re: Geometric Series Sum (Hoping somebody can check my work)

    Geometric Series Sum (Hoping somebody can check my work)-untitled.png
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