MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Determine the behavior of the series n=0∑∞n!3n.
(a) It converges conditionally because the ratio of successive terms approaches 0.
(b) It diverges because the ratio of successive terms approaches 3.
(c) It converges absolutely because the ratio of successive terms approaches 0.
(d) It diverges because the n-th term approaches 0, which therefore implies divergence.