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Math Help - Huh? Ratio test contradicts root test?

  1. #1
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    Huh? Ratio test contradicts root test?

    Find the interval of convergence for [(xn)^n]/(2^n * n!)

    I've actually tried both methods but they contradict each other! For the root test I got x = 0 and for the ratio test I got x = e/2.




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  2. #2
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    Quote Originally Posted by Kaitosan View Post
    Find the interval of convergence for [(xn)^n]/(2^n * n!)

    I've actually tried both methods but they contradict each other! For the root test I got x = 0 and for the ratio test I got x = e/2.
    Do you understand that \left( {\sqrt[n]{{\frac{{n^n }}{{n!}}}}} \right) \to e~?
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  3. #3
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    LOL. I suppose that's my mistake. I thought it was one because the exponent turns into zero. Oh well. Hey, will you please explain how that expression equals zero? Thanks.
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  4. #4
    MHF Contributor matheagle's Avatar
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    try (rod) stirling's approximation of n!
    http://en.wikipedia.org/wiki/Stirling's_approximation
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  5. #5
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    Jeez, I had no idea of this stuff. Thanks guys.
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