A sequence (n)-1 is said to oscillate if lim inf n

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.1: Sequences And Summation Notation
Problem 1E: A sequence is a function whose domain is ____________.
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A sequence (n)-1 is said to oscillate if lim inf xn <lim suprn and both lim inf n
and lim sup en are finite. Prove or disprove the following.
(a) Every oscillating sequence diverges.
(b) Every divergent sequence oscillates.
(c) Every oscillating sequence has a convergent subsequence.
Transcribed Image Text:A sequence (n)-1 is said to oscillate if lim inf xn <lim suprn and both lim inf n and lim sup en are finite. Prove or disprove the following. (a) Every oscillating sequence diverges. (b) Every divergent sequence oscillates. (c) Every oscillating sequence has a convergent subsequence.
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