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Suppose that {xn} is an unbounded sequence and x, > 0, n E N. Prove that there is a subsequence n=1 1 {xng }1 of {xn} such that lim k→o Xnk = 0. =D1

Suppose that {xn} is an unbounded sequence and x, > 0, n E N. Prove that there is a subsequence n=1 1 {xng }1 of {xn} such that lim k→o Xnk = 0. =D1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that {x,}, is an unbounded sequence and x, > 0, n E N. Prove that there is a subsequence n=1 1 {xng}1 of {x,}, such that lim = 0. k0o Xnk 100 n Sn=1
Transcribed Image Text:Suppose that {x,}, is an unbounded sequence and x, > 0, n E N. Prove that there is a subsequence n=1 1 {xng}1 of {x,}, such that lim = 0. k0o Xnk 100 n Sn=1
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