Decide whether the series converges or diverges

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

Problem

Decide whether the series ∑n=1∞(n!)1/nn3/2\displaystyle \sum_{n=1}^{\infty} \frac{(n!)^{1/n}}{n^{3/2}} converges or diverges. Provide your conclusion only.

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