For a series to have any chance of converging

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

Problem

For a series ∑n=1∞an\displaystyle\sum_{n=1}^{\infty} a_n to have any chance of converging, which of the following must be true? (a) ∣lim⁡n→∞an∣<1\displaystyle \Bigl|\lim_{n\to\infty} a_n\Bigr| < 1 (b) lim⁡n→∞an=1\displaystyle \lim_{n\to\infty} a_n = 1 (c) lim⁡n→∞an=0\displaystyle \lim_{n\to\infty} a_n = 0 (d) lim⁡n→∞an\displaystyle \lim_{n\to\infty} a_n exists and is finite

Related theory

Browse the problem library