I'm having a mind blank, can someone show that this series is convergent.
((k+2)^2)/k! summed from k=1 to infinity
Cheers
Putting $\displaystyle a_k=\frac{(k+2)^2}{k!}$ , we get that $\displaystyle \lim_{k \rightarrow \infty}\frac{a_{k+1}}{a_k}=0$ , so the quotient test solves the problem.