Problem: Find the limit of the sequence(adsbygoogle = window.adsbygoogle || []).push({});

[tex]a_{n}=\frac{n^{2}2^{n}}{n!}[/tex]

My first thought was to say that

[tex]0\leq \frac{n^{2}2^{n}}{n!} \leq \frac{x^n}{n!} [/tex]

and by squeeze theorem, since [tex]\frac{x^n}{n!}=0[/tex] for all real x, my original limit must be 0 as well. Now all I need to do is prove that [tex]n^{2}2^{n} \leq x^n[/tex], which is where I'm stuck. Can anyone give me a hand? Thanks.

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# Homework Help: Limit of a sequence

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