# Evaluate <munder> <mo movablelimits="true" form="prefix">lim <mrow class="MJX-TeXAtom-ORD

Evaluate $\underset{n\to \mathrm{\infty }}{lim}\frac{{e}^{{n}^{2}}}{\left(2n\right)!}$
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Alexzander Bowman
perhaps it becomes clearer that the limit is infinite, making the series expansion of the exponential
$\frac{{e}^{{n}^{2}}}{\left(2n\right)!}=\frac{\sum _{m=0}^{\mathrm{\infty }}\frac{\left({n}^{2}{\right)}^{m}}{m!}}{\left(2n\right)!}\ge \frac{{n}^{4n}}{\left(\left(2n\right)!{\right)}^{2}}={\left(\frac{{n}^{2n}}{\left(2n\right)!}\right)}^{2}$
the last expression on the right is $\ge Cn$ $C>0$ for large n.