Convergence of $a_n=\frac{n^{2+n}}{n!}$
I used the ratio test and have:
$\lim_{n\to\infty} \frac{(n+1)^{3+n}}{(n+1)!}\cdot \frac{n!}{(n+1)^{2+n}} \\= \lim_{n\to\infty} \frac{(n+1)^{3+n}}{n+1}\cdot \frac{1}{(n+1)^{2+n}}\\= 1$
Did I do something wrong? Correct answer appears to be $...=\lim_{n\to\infty}(1+\frac{1}{n})^{n+2}=e$