ρ= lim a(n+ 1)/a(n)= 1/3

∴ The convergence radius is R= 1/ρ=3.

When x=3, the series becomes ∑( 1/n).

At this time, the series diverges;

When x=-3,

The sequence becomes ∑ (- 1) n 1/n,

At this point the series converges.

Leibniz convergence method based on staggered series

To sum up, the convergence domain is [-3,3]