Consider the three series below

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the three series below. For each series, decide whether the value of

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

by itself rules out convergence. List all letters for which convergence is impossible on that basis alone. A.

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

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

\displaystyle \sum_{n=1}^{\infty} \frac{5}{n^{2}+1}