For a real constant

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

Problem

For a real constant α\alpha, examine the series ∑n=0∞α+n24n (x−2)n.\sum_{n=0}^{\infty} \frac{\alpha+n^{2}}{4^{n}}\,(x-2)^{n}. Determine the radius of convergence and the closed interval of xx-values on which the series fails to converge.

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