Compute and determine the implication for convergence or divergence of the series .

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

Problem

Compute lim⁡n→∞n(n+1−n)\displaystyle\lim_{n\to\infty} \sqrt{n}\bigl(\sqrt{n+1}-\sqrt{n}\bigr) and determine the implication for convergence or divergence of the series ∑n=1∞n(n+1−n)\displaystyle\sum_{n=1}^{\infty} \sqrt{n}\bigl(\sqrt{n+1}-\sqrt{n}\bigr).

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