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Math Help - convergent or divergent?

  1. #1
    Member akhayoon's Avatar
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    convergent or divergent?

    \sum\frac{k^{k/2}}{k!}

    I'm trying to figure out whether this is convergent or divergent..but the thing that is confusing me here is the k^{k/2}
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    Quote Originally Posted by akhayoon View Post
    \sum\frac{k^{k/2}}{k!}

    I'm trying to figure out whether this is convergent or divergent..but the thing that is confusing me here is the k^{k/2}
    Note, \left| \frac{n^{n/2}}{n!} \right|^{1/n} = \frac{\sqrt{n}}{(n!)^{1/n} } = \frac{1}{\sqrt{n}}\cdot \frac{n}{(n!)^{1/n}} \to 0 because (n!)^{1/n}/n \to e. Thus, by root test this converges.
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