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Math Help - partial sums of series

  1. #1
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    partial sums of series

    Consider the series . Let 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.
    S_4  = \frac{{10}}<br />
{8} + \frac{{10}}<br />
{9} + \frac{{10}}<br />
{{10}} + \frac{{10}}<br />
{{11}} = ?<br />
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  3. #3
    Member Mauritzvdworm's Avatar
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    you could use brute force to attack the problem...
    s_{1}=10(\frac{1}{8})
    s_{2}=10(\frac{1}{9}+\frac{1}{8})
    ...
    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
    \sum^{\infty}_{n=1}\frac{10}{n+7}
    should diverge since
    \sum^{\infty}_{n=1}\frac{1}{n} diverges
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