Find the interval of convergence of (x^n)/(n +1)

[Painguy]

Homework Statement

My main issue here is that if I use the ratio test I end up with lim (x(n!+1))/((n+1)!+1) n-> ∞

I don't know how to progress here. I believe that the limit will equal 0 and so it's interval of convergence is from -∞<x<∞ with a Radius of convergence of ∞. Is it safe for me to assume that?

Homework Equations

The Attempt at a Solution

 

[ehild]

It is never safe to assume anything. Prove it.

ehild

 

[Painguy]

It is never safe to assume anything. Prove it.

ehild

Well that's why I was asking. I'm not sure how to deal with the factorials here.

 

[ehild]

Well, do you know what n! is?

ehild