Let be a real number

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

Problem

Let

k

be a real number. Consider the series

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

Which of the following sets of

k

–values guarantees that the series diverges? (a) All real numbers

k

except

k=-1

(b)

k>0

only (c) All real numbers

k

(d) No real number

k

; the series converges for every

k