Find the radius and the interval of convergence of the power series

Question

summation from n=1 to infinity

(x-2)ⁿ)/((2ⁿ)(3n+2)²

Answer 1

The limiting ratio is (x-2)/2, which tells us that the radius is 2. The interval of convergence is [0, 4] and the radius is 2. We include the endpoints because (3n+2) is to a power greater than 1.