Determine whether the series converges absolutely

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

Problem

Determine whether the series ∑n=1∞(−1)n−1 n!nn\displaystyle\sum_{n=1}^{\infty} (-1)^{n-1}\,\dfrac{n!}{n^{n}} converges absolutely, converges conditionally, or diverges. State your conclusion.

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