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(b) Let X and explain whether the sequence X = (Xn) converges or diverges. (xn) be defined by xn = (-1)" n + 1 Find lim sup xn and lim inf xn %3D

(b) Let X and explain whether the sequence X = (Xn) converges or diverges. (xn) be defined by xn = (-1)" n + 1 Find lim sup xn and lim inf xn %3D

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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Real Analysis 1- Using the 2nd photo solution as an example, solve similarly the problem 4B

4. Choose and work either (a) or (b), NOT BOTH. 2n2 +3 (a) Use the definition to prove that the sequence X = (xn), where xn = %3D n2 +1 converges to 2. (b) Let X = (xn) be defined by n = (-1)"- n +1 Find lim sup xn and lim inf xn and explain whether the sequence X = (En) converges or diverges. %3D
Transcribed Image Text:4. Choose and work either (a) or (b), NOT BOTH. 2n2 +3 (a) Use the definition to prove that the sequence X = (xn), where xn = %3D n2 +1 converges to 2. (b) Let X = (xn) be defined by n = (-1)"- n +1 Find lim sup xn and lim inf xn and explain whether the sequence X = (En) converges or diverges. %3D
5. show hat. X-(), where xaz 1. 3. .--Qn~) Conveges 2.4. -(24) with out frinding Tts limik 1-3.5..... (2n-1)(zn+) (2n) (zn+2) (2n-) 2.4.6. %3B For nGN メn 1.3-5. 2.4.6.41 1.3.5..24)(2ne) (am)(2nt2) 2nt ニ 2ntl <zu+2. メn てtMて theuve, AntiLXn f all nEN. T hes the fegnence X=(X7Bmonotone decreasung. 1.3.5.00-(2n) 2.4.6.-.62) SancenG N,An X=Xn) B bownded belw (b0). So X=K) B monotonedecreasing mcT, X-(X) and borwdud belus by Mhe must Conrerg.
Transcribed Image Text:5. show hat. X-(), where xaz 1. 3. .--Qn~) Conveges 2.4. -(24) with out frinding Tts limik 1-3.5..... (2n-1)(zn+) (2n) (zn+2) (2n-) 2.4.6. %3B For nGN メn 1.3-5. 2.4.6.41 1.3.5..24)(2ne) (am)(2nt2) 2nt ニ 2ntl <zu+2. メn てtMて theuve, AntiLXn f all nEN. T hes the fegnence X=(X7Bmonotone decreasung. 1.3.5.00-(2n) 2.4.6.-.62) SancenG N,An X=Xn) B bownded belw (b0). So X=K) B monotonedecreasing mcT, X-(X) and borwdud belus by Mhe must Conrerg.
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