For a series

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

Problem

For a series ∑n=1∞an\sum_{n=1}^{\infty} a_n, the limit lim⁡n→∞an\displaystyle\lim_{n\to\infty} a_n is evaluated. Which of the following conclusions is always valid? (a) If lim⁡n→∞an=0,\displaystyle\lim_{n\to\infty}a_n=0, the series must converge. (b) If the limit is non-zero or does not exist, the series diverges. (c) If lim⁡n→∞an=∞,\displaystyle\lim_{n\to\infty}a_n=\infty, the series may converge. (d) If the limit does not exist, no conclusion can be drawn about convergence.

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