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Thread: convergence of sum

  1. #1
    Senior Member Dinkydoe's Avatar
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    convergence of sum

    Hoi, is there a way we can conclude that

    $\displaystyle \lim_{n\to\infty}\frac{a_1+\cdots + a_n }{n} = \infty$ from the assumption that for some positive constant $\displaystyle K$

    $\displaystyle \lim_{n\to\infty}\frac{\log(a_1)+\cdots \log(a_n)}{n} = K$

    I need it for something, but i'm not even sure if it's true...?

    The $\displaystyle a_n\geq 1$ are positive integers.
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  2. #2
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    Re: convergence of sum

    Suppose $\displaystyle a_n = 2$. Then what?
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  3. #3
    Senior Member Dinkydoe's Avatar
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    Re: convergence of sum

    ehm...ur right. its not true XD
    Last edited by Dinkydoe; Nov 6th 2012 at 01:57 PM.
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