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Math Help - Converging series

  1. #1
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    Converging series

    Determine which of the following series, , converge

    i)

    ii)
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  2. #2
    Moo
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    Hello,

    For any x, sin^2(x)+cos^2(x)=1

    So in ii), a_n=1 and \sum_1^\infty 1 is known to diverge
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  3. #3
    Super Member angel.white's Avatar
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    Quote Originally Posted by matty888 View Post
    a_n = \frac {n^2}{n!} = \frac {n}{(n-1)!}

    Using the Ratio test:
    \lim_{n->\infty} \left| \frac{a_{n+1}}{a_n}\right| = \lim_{n->\infty} \left| \frac{n+1}{n!}*\frac{(n-1)!}{n}\right|

    =\lim_{n->\infty} \left| \frac{n+1}{n^2}\right|

    =\lim_{n->\infty} \left| \frac{1+\frac 1n}{n}\right|

    =0

    0 < 1 therefore the series is absolutely convergent and therefore convergent.
    Quote Originally Posted by Moo View Post
    \sum_1^\infty 1 is known to diverge
    Not sure if that was a joke, but it was rather amusing ^_^
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  4. #4
    Moo
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    o.O

    I was kinda serious, it diverges, doesn't it ?
    The non-serious part was "known to", it depends on the level of the matty888 ^^
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