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CalculusChallengeInfinite Sequences and Series

Infinite Sequences and Series · Challenge problem

For how many integers xx does the series ∑n=1∞n (x−2)n(n2+1) 3n\displaystyle\sum_{n=1}^{\infty}\frac{n\,(x-2)^n}{(n^2+1)\,3^n} converge?