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. For which values of

k

does the series

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

converge? (a) Only for

k>1

(b) Only for

k<0

k

(d) For no real value of

k