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Math Help - Why does this converge ?

  1. #1
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    Why does this converge ?

    \sum (-1)^{k+1} * \frac {1} {k}

    k starts at 1 and sum goes to infinity

    since 1/k is diverging and its limit is infinity, why does the series converge ? isnt it necessary for an alternating series to go strictly to 0 as k approaches infinity to be a convergent series ?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by coobe View Post
    \sum (-1)^{k+1} * \frac {1} {k}

    k starts at 1 and sum goes to infinity

    since 1/k is diverging and its limit is infinity, why does the series converge ? isnt it necessary for an alternating series to go strictly to 0 as k approaches infinity to be a convergent series ?
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  3. #3
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    1/k does not diverge to infinity, it converges to 0
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by shayan603 View Post
    1/k does not diverge to infinity, it converges to 0
    He obviously meant the harmonic series.
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  5. #5
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    so the harmonic series does diverge while the alternating harmonic series converge ?
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by coobe View Post
    so the harmonic series does diverge while the alternating harmonic series converge ?
    True dat.
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