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Math Help - Multiplication of two series...

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Multiplication of two series...

    Multiply these two series:

    (1) \Sigma^{\infty}_{n=1} \frac{1}{2^{n-1}}

    (2) \Sigma^{\infty}_{n=1} \frac{1}{n\sqrt{n}}
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  2. #2
    Member mfetch22's Avatar
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Multiply these two series:

    (1) \Sigma^{\infty}_{n=1} \frac{1}{2^{n-1}}

    (2) \Sigma^{\infty}_{n=1} \frac{1}{n\sqrt{n}}
    I believe the first series is equal to 2, correct? So wouldn't that imply that we just multiply each term in the second series by 2? I'm not certain, because I have no experience with multiplying infinite series, but wouldn't the result (since the first series is equal to 2) simply be:

    \Sigma^{\infty}_{n=1} \frac{2}{n\sqrt{n}}

    ?
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Oooops...
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