If , what conclusion can be drawn about the series…

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

Problem

If lim⁡n→∞an≠0\displaystyle\lim_{n\to\infty} a_n \neq 0, what conclusion can be drawn about the series ∑n=1∞an\sum_{n=1}^{\infty} a_n? (a) It converges if the terms alternate in sign. (b) It must diverge. (c) It diverges only if lim⁡n→∞an=∞\displaystyle\lim_{n\to\infty} a_n = \infty. (d) It may converge or diverge; the test is inconclusive.

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