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Math Help - Evaluate sum to 'n' terms(Sequences and Series)?

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    Super Member fardeen_gen's Avatar
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    Evaluate sum to 'n' terms(Sequences and Series)?

    Evaluate sum of n terms of the series:

    \frac{8}{5} + \frac{16}{65} + \frac{24}{325} + \mbox{... till n terms}
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    Moo
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    Hello,
    Quote Originally Posted by fardeen_gen View Post
    Evaluate sum of n terms of the series:

    \frac{8}{5} + \frac{16}{65} + \frac{24}{325} + \mbox{... till n terms}
    So the numerator is 8n, but the denominator ??

    5
    5x13
    5x5x13

    what's the pattern ? is it possible to get more terms ?
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    Super Member fardeen_gen's Avatar
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    I do not know Does anybody see the trick?
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    Moo
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    Okay, one possibility would be 5^{\lfloor \frac{n+1}{2}\rfloor}13^{\lfloor \frac n2\rfloor}



    so then you can make the difference between odd and even terms...
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    Super Member fardeen_gen's Avatar
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    Quote Originally Posted by Moo View Post
    Okay, one possibility would be 5^{\lfloor \frac{n+1}{2}\rfloor}13^{\lfloor \frac n2\rfloor}



    so then you can make the difference between odd and even terms...
    Difference between odd and even terms? Could you explain?
    Last edited by fardeen_gen; May 21st 2009 at 11:26 AM.
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    Moo
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    Quote Originally Posted by fardeen_gen View Post
    Difference between odd and even terms? Could you explain?
    Vocabulary problem I meant separate.

    The even terms in the form 2k will be 5^k13^k
    The odd terms in the form 2k+1 will be 5^{k+1}13^k

    Then, I guess you'll have a different result, depending on whether n is odd or even.
    I don't see a shortcut for the moment. And it doesn't look nice
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