Answer
$\frac{5}{12}$.
Work Step by Step
Since we have
$$\lim_{n\to \infty}b_n=\lim_{n\to \infty}\frac{5n-1}{12n+9}=\lim_{n\to \infty}\frac{5-(1/n)}{12+(9/n)}=\frac{5}{12}$$
then the sequence $b_n$ converges to $\frac{5}{12}$.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 11 - Infinite Series - 11.1 Sequences - Exercises - Page 537: 17
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