Which of the following infinite series diverges?

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

Problem

Which of the following infinite series diverges? (a)

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

(b)

\displaystyle \sum_{k=0}^{\infty} \left( \tfrac43 \right)^{k}

(c)

\displaystyle \sum_{k=1}^{\infty} \frac{1}{k^{2}}

(d)

\displaystyle \sum_{k=1}^{\infty} \frac{k}{2^{k}}