A sequence is defined recursively by and for

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

A sequence is defined recursively by

a_1=2

and

a_{n+1}=\dfrac{3a_n+1}{4}

for

n\ge 1

. Using the behavior of

a_n

n\to\infty

, determine whether the series

\displaystyle \sum_{n=1}^{\infty} a_n

converges or diverges.