For real parameter

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

Problem

For real parameter

k

, define

a_n(k)=\begin{cases}\dfrac{1}{n}, & n\text{ even},\\[6pt]-\dfrac{k}{n}, & n\text{ odd}.\end{cases}

For which values of

k

does the infinite series

\displaystyle\sum_{n=1}^{\infty} a_n(k)

converge? (a)

k<1

(b)

k=1

(c)

k>1

(d) All real

k