12.4 Show lim sup(sn +tn) < lim sup s, +lim sup tn for bounded sequences (Sn) and (tn). Hint: First show sup{sn + tn : n > N} < sup{sn :n > N}+sup{tn :n > N}.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 34E
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12.4 Show lim sup(sn+tn) < lim sup sn +lim sup t, for bounded sequences
(Sn) and (tn). Hint: First show
sup{sn + tn : n > N} < sup{Sn : n > N} +sup{tn : n > N}.
Transcribed Image Text:12.4 Show lim sup(sn+tn) < lim sup sn +lim sup t, for bounded sequences (Sn) and (tn). Hint: First show sup{sn + tn : n > N} < sup{Sn : n > N} +sup{tn : n > N}.
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