Mathematics

Mathematics

Problem

The partial sums SnS_n of a certain infinite series satisfy S1<S2<S3<…S_1< S_2< S_3<\dots and Sn<9S_n<9 for every positive integer nn. 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 99, 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 ana_n approach 00 faster than 1n\dfrac{1}{n}.}],

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