For real numbers

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

Problem

For real numbers

k

, examine the series

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

. Based only on the behavior of its

n

th term, for which values of

k

can the convergence of the series be ruled out? (a)

k>1

(b)

k\ge 0

(c)

k>0

(d)

k\ge -1