Consider the series _ n=2 ^ 5n^ 5 +7 2n^ 7 -n

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

Problem

Consider the series

\sum_{n=2}^{\infty}\frac{5n^{5}+7}{2n^{7}-n}.

Which statement about this series is correct? (a) It diverges because its terms behave like

\dfrac{1}{n}

. (b) It converges because the terms approach

0

n\to\infty

. (c) It diverges by the Ratio Test since the limit of consecutive terms equals

1

. (d) It converges by comparison with a

p

-series whose exponent satisfies

p>1