Mathematics

Problem

The power series

\displaystyle \sum_{n=0}^{\infty} a_n x^n

converges for

|x|<5

. State the inequality that must be satisfied by

x

for the transformed series

\displaystyle \sum_{n=0}^{\infty} a_n \bigl(x^{2}-1\bigr)^{n}

to converge, and briefly explain why this condition follows from the original radius of convergence.