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Math Help - Series equation

  1. #16
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    Re: Series equation

    so I get  \frac{4}{3} S , which is great but how the S looks? How to make all idices the same?
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  2. #17
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    Re: Series equation

    Quote Originally Posted by Lisa91 View Post
    so I get  \frac{4}{3} S , which is great but how the S looks? How to make all idices the same?
    Indexes have no impact on the outcome of the sum so you call all of them k or r or m or f or g or whatever you want!
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  3. #18
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    Re: Series equation

    Well... We have 3 \sum_{m=1}^{\infty} \frac{1}{m3^{m}} - 1-\frac{1}{6} +\frac{1}{3} \sum_{k=1}^{\infty} \frac{1}{k3^{k}}-2\sum_{n=1}^{\infty} \frac{2}{n3^{n}} . Then we get  \frac{4}{3}\sum_{n=1}^{\infty} \frac{1}{n3^{n}} -\frac{7}{6} which is wrong. We should get  -\frac{1}{2} .
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  4. #19
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    Re: Series equation

    Quote Originally Posted by Lisa91 View Post
    So, I got \sum_{m=1}^{\infty} \frac{3}{m3^{m}} - \frac{7}{6} + \frac{1}{3}\sum_{k=1}^{\infty} \frac{1}{k3^{k}} - \sum_{n=1}^{\infty} \frac{2}{n3^{n}} How to combine them all? I don't know how to cope with those  2,3, \frac{1}{3} . For instance, if I go back to n, I get n=0 in the first term, which is not what I want...
    Here's the mistake. The last one should have began from n = 2 (since we didn't do anything to it). So write it from n = 1 by subtracting the value at n = 1.
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  5. #20
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    Re: Series equation

    Thank you all so much! Now it's ok
    Thanks from TheSaviour
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