Three series are given

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

Problem

Three series are given. I.

\displaystyle \sum_{n=1}^{\infty}\frac{n^{2}}{n^{2}+1}

II.

\displaystyle \sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}}

III.

\displaystyle \sum_{n=1}^{\infty}\frac{2n}{n+1}

Which of the series diverge based on the behavior of their

n

th terms? (a) III only (b) I only (c) I and III only (d) I, II, and III