show that If an > 0, n = 1, 2,. .... In+1 In+1 lim inf 14x

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 13E: Let and . Prove or disprove that .
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If an > 0, n = 1, 2,..., show that
Xn+1
In+1
lim inf
<lim inf n ≤ lim sup n ≤ lim sup
n4x
In
n-x
n→∞
n→∞
In
In+1
exists, then limnon exists. What happened to the converse?
Deduce that if lim
n-∞ In
Transcribed Image Text:If an > 0, n = 1, 2,..., show that Xn+1 In+1 lim inf <lim inf n ≤ lim sup n ≤ lim sup n4x In n-x n→∞ n→∞ In In+1 exists, then limnon exists. What happened to the converse? Deduce that if lim n-∞ In
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