Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - 11.1 Sequences - 11.1 Exercises - Page 745: 71


$5 \leq L \lt 8$

Work Step by Step

Given that {$a_{n}$} is a decreasing sequence $ a_{n} \gt a_{n+1} \gt a_{n+2} \gt a_{n+3} \gt ...$ for all $n\geq 1$ {$a_{n}$} is a bounded sequence since all terms lie between 5 and 8. By Monotonic sequence theorem, {$a_{n}$} is convergent {$a_{n}$} has a limit $L$. Since 8 is an upper bound of {$a_{n}$}, $L$ must be less than 8. $5 \leq L \lt 8$
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