Converging series with factorials

It's been a while since calculus and this problem actually is part of probability theory question. I've got the answer down into a series.

∑(1.5^n)/[n*(n-2!)] = ∑[(1.5^n)*(n-1)]/(n!)

both summations from n=2 to infinity. (I proved that both sides are equal, just didn't know which would be easier to solve)

I can see that the denominator will increase much faster than the numerator, leading me to believe that this series will converge. I also verified it by the ratio test and I also computed it in Excel. Without having Excel or a calculator, how can you solve this series by hand?

From Excel, the series converges to 3.24084453516903.