Find general term of $1+\frac{2!}{3}+\frac{3!}{11}+\frac{4!}{43}+\frac{5!}{171}+....$ 
Find general term of $1+\frac{2!}{3}+\frac{3!}{11}+\frac{4!}{43}+\frac{5!}{171}+....$

However it has been ask to check convergence but how can i do that before knowing the general term. I can't see any pattern,comment quickly!

Hint

The numerator is easy.
For the denominator, see the succesive differences. If you still can't figure out see Arithmetico–geometric sequence.

