Let be a real number

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

Problem

Let xx be a real number. For which values of xx does the series ∑n=1∞n! xnnn\displaystyle \sum_{n=1}^{\infty} \dfrac{n!\,x^{n}}{n^{n}} converge? (a) ∣x∣<1/e|x|<1/e (b) ∣x∣<1|x|<1 (c) ∣x∣<e|x|<e (d) ∣x∣≤e|x|\le e

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