Determine the interval of convergence for the power series

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Determine the interval of convergence for the power series ∑n=0∞n2(x−1)n4 n\displaystyle \sum_{n=0}^{\infty}\frac{n^{2}(x-1)^{n}}{4^{\,n}}. State clearly which endpoints, if any, are included in the interval.

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