Which of the following statements best describes what the th-term test can tell you…

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

Problem

Which of the following statements best describes what the nnth-term test can tell you about an infinite series ∑an\displaystyle\sum a_n? (a) If lim⁡n→∞an=0\displaystyle\lim_{n\to\infty} a_n=0, the series converges absolutely. (b) The nnth–term test decides whether a series is conditionally or absolutely convergent based solely on whether lim⁡n→∞an\displaystyle\lim_{n\to\infty} a_n is zero. (c) If lim⁡n→∞an≠0\displaystyle\lim_{n\to\infty} a_n\neq 0 or the limit does not exist, the series diverges; if lim⁡n→∞an=0\displaystyle\lim_{n\to\infty} a_n = 0, the test is inconclusive. (d) If lim⁡n→∞an≠0\displaystyle\lim_{n\to\infty} a_n\neq 0, the series converges; if lim⁡n→∞an=0\displaystyle\lim_{n\to\infty} a_n = 0, the series diverges.

Related theory

Browse the problem library