The partial sums of a certain infinite series satisfy and for every positive integer
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
The partial sums Sn of a certain infinite series satisfy S1<S2<S3<… and Sn<9 for every positive integer n. Which statement best describes the series?
(a) The series diverges because its partial sums increase without bound.
(b) The series diverges because the limit of the partial sums is 9, which is not zero.
(c) The series converges because its partial sums form a monotone increasing sequence that is bounded above.
(d) The series converges because the terms an approach 0 faster than n1.}],