Consider the series _ n=1 ^ 3^ n 4^ n +1

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

Problem

Consider the series

\sum_{n=1}^{\infty} \frac{3^{n}}{4^{n}+1}.

What can be concluded from the

n

th term test? (a) The series diverges because the limit of its terms is

\dfrac{3}{4}

. (b) The series converges because the limit of its terms is 0. (c) The

n

th term test is inconclusive because the limit of its terms is 0. (d) The series converges by comparison to a geometric series with ratio

\dfrac{3}{4}