# Math Help - Convergent series

1. ## Convergent series

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

2. Hmm i think I got it. Ratio test =0 so converges

3. Originally Posted by Sam1111
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 $a_k=\frac{(k+2)^2}{k!}$ , we get that $\lim_{k \rightarrow \infty}\frac{a_{k+1}}{a_k}=0$ , so the quotient test solves the problem.

Tonio