The th partial sum of an infinite series is

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

\displaystyle S_n=\frac{3n^{2}+2n}{n^{2}+4n+4}

. Determine the value to which the series converges, if it converges. (a) The series converges to

\dfrac34

. (b) The series converges to

3

. (c) The series converges to

0

. (d) The series diverges because

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