Question

What is the interval of convergence of #sum_1^oo ((3x-2)^2)/(n*x*3^n) #?

Answer 1

Is convergent for all `x ne 0`

Explanation:

This power series is equivalent to
`(3x-2)^2/x sum_{n=1}^{infty}1/(i 3^i)`. The sum `sum_{n=1}^{infty}1/(i 3^i)` is convergent to a real number `C_0` so the power series is
equivalent to `C_0 (3x-2)^2/x` which is convergent for all `x ne 0`