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Math Help - convergence of a series

  1. #1
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    convergence of a series

    Does the series SIGMA (0 to infinity) r!/r^2(e^r) converge or diverge and why?

    Tried using the ratio test and got to lim (r tend to inf) r^2/(r+1)e , which equals infinity(?). sooo it diverges as its greater than 1?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    You are correct
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  3. #3
    Senior Member Shanks's Avatar
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    By the Stirling formula, \frac{r!}{r^2e^r} does not tend to 0 as r approches infinity, thus the series diverges.
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