The sequence of partial sums of an infinite series satisfies

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

Problem

The sequence of partial sums

(S_n)

of an infinite series satisfies

\displaystyle\lim_{n\to\infty} S_n = 7

. Which statement is most accurate about the infinite series? (a) The series diverges, because the limit of the partial sums is not

0

. (b) Whether the series converges or diverges cannot be decided; we must first verify that

\displaystyle\lim_{n\to\infty} a_n = 0

. (c) The series converges, and its sum equals 7. (d) The series converges, but its exact sum cannot be determined from the given partial sums.