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Thread: partial sums of series

  1. #1
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    partial sums of series

    Consider the series . Let $\displaystyle s_n$ be the n-th partial sum; that is,

    s4=
    s8=

    can someone help me with this one
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  2. #2
    MHF Contributor

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    This is just plug and chug. You got to do for yourself.
    $\displaystyle S_4 = \frac{{10}}
    {8} + \frac{{10}}
    {9} + \frac{{10}}
    {{10}} + \frac{{10}}
    {{11}} = ?
    $
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  3. #3
    Member Mauritzvdworm's Avatar
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    you could use brute force to attack the problem...
    $\displaystyle s_{1}=10(\frac{1}{8})$
    $\displaystyle s_{2}=10(\frac{1}{9}+\frac{1}{8})$
    ...
    $\displaystyle s_{4}=10(\frac{1}{11}+\frac{1}{10}+\frac{1}{9}+\fr ac{1}{8})$

    there could be a simpler way, the only thing bothering me is that
    $\displaystyle \sum^{\infty}_{n=1}\frac{10}{n+7}$
    should diverge since
    $\displaystyle \sum^{\infty}_{n=1}\frac{1}{n}$ diverges
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