Consider the series

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

Problem

Consider the series

S=\displaystyle \sum_{n=0}^{\infty}\dfrac{5}{3^{n}+7}

. Which of the following statements is correct? (a)

S

diverges because

\displaystyle \frac{5}{3^{n}+7}>\frac{1}{n}

for sufficiently large

n

. (b)

S

diverges since

\displaystyle\lim_{n\to\infty}\frac{5}{3^{n}+7}\neq 0

. (c)

S

converges to a finite sum. (d)

S

diverges by the ratio test because the ratio of successive terms exceeds

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