Find the radius of convergence of the series from n=0 to infinity of ((9x-4)^(2n+1))/(n^(3/2)).

Question

I think it is 5/9.

Answer 1

the n=0 term makes it diverge.
However, summing from 1 to infinity

As for the radius, you want 1/3 < x < 5/9
because you need (4-9x)^2 < 1 not just (4-9x)<1