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Math Help - Analysis - Series

  1. #1
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    Analysis - Series

    The question is i need to prove the following series converge or diverge,
    for the first part i get (e^-3+5)/5 which is bigger than 1 so it diverges and for the second part i get 1 ( so is this wrong as a series diverges if it is less than 1 and converges if it is more than 1,or is it a special case)

    Any help would be much appreciated
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  2. #2
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    Quote Originally Posted by asingh88 View Post
    The question is i need to prove the following series converge or diverge,
    for the first part i get (e^-3+5)/5 which is bigger than 1 so it diverges and for the second part i get 1 ( so is this wrong as a series diverges if it is less than 1 and converges if it is more than 1,or is it a special case)

    Any help would be much appreciated

    \frac{e^{-3n}}{(2n)^n+5}\leq \frac{1}{2^n}

    \frac{5n}{n^3+n^2}=\frac{5}{n^2+n}\leq \frac{5}{n^2}


    Now use the comparison test and we're through.

    Tonio
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