9000064008

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