Radius and interval of convergence

Hi, I'm trying to do this question, but I'm stuck.

Find the radius and interval of convergence of the series:

x^2n/(n(ln(n))^2)

The summation from 2 to inifinity.


I applied the ratio test and got that the limit equals abs(1/x^2). Applying the inequality I got abs(1/x^2) < 1.

I'm stuck here, because shouldn't the radius of convergence be 1? According to the inequality, the series will converge on two intervals: [-inf, -1) and (1, inf].

Some help would be greatly appreciated.

Because is and the series...

(1)

... converges for , also the series...

(2)

... converges for . Ther only difference is that the series (2), unlike the (1), converges also for ...

Kind regards