The th partial sum of an infinite series is given by

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

Problem

The

n

th partial sum of an infinite series is given by

S_n=4-\dfrac{3}{n}+\dfrac{(-1)^n}{2n}

. What can be concluded about the series? (a) It diverges because the partial sums oscillate indefinitely. (b) It converges, and the series sums to

4

. (c) It converges, and the series sums to

4.5

. (d) It diverges because the terms of the series do not tend to zero.