Science:Math Exam Resources/Courses/MATH101/April 2017/Question 11 (c)/Statement

Let $A_n$ be a sequence of positive numbers such that the power series $\sum _{n=0}^{\mathrm{\infty }}{A}_n(x-1{)}^n$ has radius of convergence $R=\frac{3}{2}$.

(c) Does the series $\sum _{n=0}^{\mathrm{\infty }}n(n-1)A_n$ converge or diverge? Justify your answer.