6. (a) For each n E N, find mn EN such that m²/2 (b) Let n <2< n² Pn - (mn + 1)² n² mn n Show that p → 2 and {pn}_1 is Cauchy. (c) Prove that the sequence {pn}_1 does not converge in Q.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 14RE
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Question
6. (a) For each n € N, find mɲ € N such that
m²/12
n²
(b) Let
<2<
Pn
=
(mn + 1)²
n²
mn
n
Show that p² → 2 and {pn}1 is Cauchy.
=1
(c) Prove that the sequence {pn}_₁ does not converge in Q.
n=
Transcribed Image Text:6. (a) For each n € N, find mɲ € N such that m²/12 n² (b) Let <2< Pn = (mn + 1)² n² mn n Show that p² → 2 and {pn}1 is Cauchy. =1 (c) Prove that the sequence {pn}_₁ does not converge in Q. n=
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