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Let {xn} be a sequence of real numbers. Is it true that if limsup(x₁) = 2, then there is n e N such that 1.99 < xn. Justify your answer Hint: Use this theorem: If {xn} is bounded above, X = limsup(xn) if and only if For all & >0 and all M, there is n > M with X - ε < Xn

Let {xn} be a sequence of real numbers. Is it true that if limsup(x₁) = 2, then there is n e N such that 1.99 < xn. Justify your answer Hint: Use this theorem: If {xn} is bounded above, X = limsup(xn) if and only if For all & >0 and all M, there is n > M with X - ε < Xn

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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Please use the theorem  to justify your answeer. Thanks

 

Let {xn} be a sequence of real numbers. Is it true that if limsup(x₁) = 2, then there is n e N such that 1.99 < xn. Justify your answer Hint: Use this theorem: If {xn} is bounded above, X = limsup(xn) if and only if For all & >0 and all M, there is n > M with X - ε < Xn
Transcribed Image Text:Let {xn} be a sequence of real numbers. Is it true that if limsup(x₁) = 2, then there is n e N such that 1.99 < xn. Justify your answer Hint: Use this theorem: If {xn} is bounded above, X = limsup(xn) if and only if For all & >0 and all M, there is n > M with X - ε < Xn
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