For the series

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

Problem

For the series ∑n=1∞(x−2)nn 2 n\displaystyle \sum_{n=1}^{\infty}\frac{(x-2)^n}{n\,2^{\,n}}, determine the interval of convergence, explicitly stating whether the series converges or diverges at each endpoint.

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