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Math Help - interval of convergence

  1. #1
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    interval of convergence

    Interval of Convergence of the following...
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  2. #2
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    Quote Originally Posted by WartonMorton View Post
    Interval of Convergence of the following...

    1) This question doesn't belong here

    2) It's practically impossible to decypher what you meant to write, in particular that weird middle symbol...??

    Tonio
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  3. #3
    MHF Contributor chisigma's Avatar
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    Under the hypothesis that is...

    f(x)= \sum_{k=1}^{\infty} k a^{k} x^{k} (1)

    ... setting a x = \xi we have...

    \sum_{k=1}^{\infty} k a^{k} x^{k}= \sum_{k=1}^{\infty} k \xi^{k}= \xi \sum_{k=1}^{\infty} k \xi^{k-1} = \xi \frac{d}{d \xi} \sum_{k=1}^{\infty} \xi^{k} =

    = \xi \frac{d}{d \xi} \frac{\xi}{1-\xi} = \frac{\xi}{(1-\xi)^{2}} (2)

    The series converges for |\xi|<1 ...

    Kind regards

    \chi \sigma
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