SUM n_infinity (-1)^n+1 (3n/n!)

I believe this is solved using the absolute ratio test.

I see where this becomes lim n -> infinity (3n+1)/(n+1)! / 3n/n!

=

lim n->infinity 3/(n +1) = 0

Is it common for this series to always divide by the original equation? what happened to the (-1)^n+1

i need some help understanding whats going on.