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Thread: Convergent series

  1. October 25th 2009, 07:34 PM #1
    Sam1111
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    Convergent series

    I'm having a mind blank, can someone show that this series is convergent.

    ((k+2)^2)/k! summed from k=1 to infinity

    Cheers
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  2. October 25th 2009, 07:37 PM #2
    Sam1111
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    Hmm i think I got it. Ratio test =0 so converges
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  3. October 25th 2009, 07:40 PM #3
    tonio
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    Quote Originally Posted by Sam1111 View Post
    I'm having a mind blank, can someone show that this series is convergent.

    ((k+2)^2)/k! summed from k=1 to infinity

    Cheers

    Putting a_k=\frac{(k+2)^2}{k!} , we get that \lim_{k \rightarrow \infty}\frac{a_{k+1}}{a_k}=0 , so the quotient test solves the problem.

    Tonio
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