the radius of convergence of of n=1 to infinity ((-1)^n+1 (x-2)^n )/n3^n

Answer 1

The absolute value of the ratio of a_n+1 to a_n is n(x-2)/[3(n+1)] which means the series converges only for

|x-2|<3. I am not sure how you express this as a "radius" of convergence.