Which of the following is a necessary condition for the infinite series to converge?

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

Problem

Which of the following is a necessary condition for the infinite series ∑n=1∞an\displaystyle\sum_{n=1}^{\infty} a_n to converge? (a) ∣an∣<1 for every n|a_n|<1\text{ for every }n (b) lim⁡n→∞an=0\displaystyle \lim_{n\to\infty} a_n = 0 (c) The sequence of partial sums {Sn}\{S_n\} is bounded below. (d) The sequence {an}\{a_n\} is strictly decreasing.

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