Mathematics

Mathematics

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.

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