Consider the power series

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the power series ∑n=0∞(x−3)n5n\displaystyle\sum_{n=0}^{\infty}\dfrac{(x-3)^{n}}{5^{n}}. Which of the following values of xx is guaranteed to make the series converge? (a) 88 (b) −3-3 (c) 11 (d) 1010

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