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Math Help - ratio

  1. #1
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    ratio

    how do you prove using ratio test that the series from n=1 to infinity of
    ((n+1)^2 )(2^n) / n! converges?


    i tried using a_n+1 over a_n but cant seem to get the answer
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  2. #2
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    The ratio test should work...
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  3. #3
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    this is what i got:

    by ratio test,

    l a_n+1 / a_n l = ((n+2)^2 )(2^n+1) / ((n+1)! ) / ((n+1)^2 )(2^n) / n!
    = [1 + 1/ (n+1) ]^2 multiply with (2) divide by (n+1)

    how can i tell that this is less than 1?
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  4. #4
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    You need to evaluate \displaystyle \lim_{n \to \infty}\left|\frac{a_{n+1}}{a_n}\right|.
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  5. #5
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    oh shucks i totally forgot about that. was too concerned with the ratios. thanks!!!
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