all x s

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.1: Sequences And Their Notations
Problem 71SE: Prove the conjecture made in the preceding exercise.
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Question
Prove that, if n is a positive integer, then
et > x" for all x sufficiently large.
HINT: e = 1+
e'dt > 1+ | dt = 1 +x
%3D
%3D
e* = 1+ | e'dt > 1+ | (1+t)dt
x2
= 1+x +
2 '
and so on.
%3D
Transcribed Image Text:Prove that, if n is a positive integer, then et > x" for all x sufficiently large. HINT: e = 1+ e'dt > 1+ | dt = 1 +x %3D %3D e* = 1+ | e'dt > 1+ | (1+t)dt x2 = 1+x + 2 ' and so on. %3D
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