Evaluate and decide

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

Problem

Evaluate lim⁡n→∞(nn+1) ⁣n\displaystyle\lim_{n\to\infty}\left(\dfrac{n}{n+1}\right)^{\!n} and decide, using that limit, whether the series ∑n=1∞(nn+1) ⁣n\displaystyle\sum_{n=1}^{\infty}\left(\dfrac{n}{n+1}\right)^{\!n} converges or diverges.

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