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

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

(b) Does the sequence $\left\{{\frac {1}{A_{n}}}\right\}$ converge or diverge? Justify your answer.