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Math Help - converge or diverge

  1. #1
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    converge or diverge

    Does the series converge or diverge the sum as n goes to infinity
    n^10/〖10〗^n .
    Thank you!
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  2. #2
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    Do you know how to use the root test?
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  3. #3
    Eater of Worlds
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    We can try the ratio test.

    \sum_{n=1}^{\infty}\frac{n^{10}}{10^{n}}

    \frac{u_{k+1}}{u_{k}}=\frac{(n+1)^{10}}{10^{n+1}}\  cdot\frac{10^{n}}{n^{10}}=\frac{(n+1)^{10}}{10n^{1  0}}

    {\rho}=\lim_{n\rightarrow{\infty}}\frac{(n+1)^{10}  }{10n^{10}}=\frac{1}{10}

    {\rho}<1

    What dies that tell you?.

    This is an interesting series. Try to find what it converges to.
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