10. Suppose that {b} is a sequence such that lim bn = 1. Show that 72-00 bn-1 lim no ln bn 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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Q
F4
2
for all nonnegative integers m≥k. If a₁ = 1, find a closed form for an
%
5
8. Let {an} be a sequence such that for all n ≥ 2 there exists an integer t
with n/2 ≤t≤n such that an = at/2. Prove that lim an = 0.
81x
9. Let {an} be defined by an = n²+2. Find a subsequence {ank} such that
if r<s, then an, divides an..
10. Suppose that {b} is a sequence such that lim bn = 1. Show that
n→∞
bn-1
lim
n→∞ ln bn
T
G
9
F5
^
6
= 1.
MacBook Air
c
F6
Y
H
&
7
←
F7
U
* 00
J
8
DII
F8
D
(
9
1
K
DD
F9
0
-O
0
F10
P
F1
Transcribed Image Text:Q F4 2 for all nonnegative integers m≥k. If a₁ = 1, find a closed form for an % 5 8. Let {an} be a sequence such that for all n ≥ 2 there exists an integer t with n/2 ≤t≤n such that an = at/2. Prove that lim an = 0. 81x 9. Let {an} be defined by an = n²+2. Find a subsequence {ank} such that if r<s, then an, divides an.. 10. Suppose that {b} is a sequence such that lim bn = 1. Show that n→∞ bn-1 lim n→∞ ln bn T G 9 F5 ^ 6 = 1. MacBook Air c F6 Y H & 7 ← F7 U * 00 J 8 DII F8 D ( 9 1 K DD F9 0 -O 0 F10 P F1
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