2010005303

Find the limit of the following sequence. $${\left(\frac{(n^2+4n+4{)}^n}{n^{2n}}\right)}_{n=1}^{\mathrm{\infty }}$$ Hint: The limit of the sequence ${\left({(1+\frac{2}{n})}^n\right)}_{n=1}^{\mathrm{\infty }}$ is ${\mathrm{e}}^2$, where $\mathrm{e}$ is the Euler number.