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Math Help - Test for convergence

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    Test for convergence

    Hey which test should I use to determine if this series converges? I'm thinking maybe a comparison test?

     \sum_{n=1}^\infty e^\frac{1}{n^9}/ n^{10}
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    Quote Originally Posted by mmattson07 View Post
    Hey which test should I use to determine if this series converges? I'm thinking maybe a comparison test?

     \sum_{n=1}^\infty e^\frac{1}{n^9}/ n^{10}
    Write back because it's hard to decide what you meant to write.

    Tonio
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    My apologies. I couldn't get the /frac to work around the whole expression. Its supposed to be e^(1/n^9) / n^10.
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    Quote Originally Posted by mmattson07 View Post
    Hey which test should I use to determine if this series converges? I'm thinking maybe a comparison test?

     \sum_{n=1}^\infty e^\frac{1}{n^9}/ n^{10}
    Perhaps an integral comparison test ....
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    So since it is positive and decreasing the Integral test applies?
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    Quote Originally Posted by mmattson07 View Post
    My apologies. I couldn't get the /frac to work around the whole expression. Its supposed to be e^(1/n^9) / n^10.

    It's not hard to check that e^{\frac{1}{n^9}}\xrightarrow [n\to \infty] {} 1, so you can use the comparison test for positives series: for n big enough, \frac{e^{\frac{1}{n^9}}}{n^{10}}\leq \frac{2}{n^{10}}...

    Tonio
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