Determine the behavior of the series .

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

Problem

Determine the behavior of the series

\displaystyle \sum_{n=4}^{\infty} \dfrac{2^{n}}{3^{n}-1}

. (a) The series diverges because the ratio

a_{n+1}/a_n

\tfrac{3}{2}>1

. (b) The series converges conditionally but not absolutely. (c) The series converges absolutely by comparison with the geometric series

\sum (2/3)^n

. (d) The series diverges because the terms do not approach

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