#4 Short proofs and counterexamples, II. As before, determine if the statement is true or false. Ifit is true, give a proof; if it is false, give a specific counterexample and explain why this example has thedesired properties.(a) If {n} converges, then for all € > 0 there exists n € N such that |xn+1 − Xn| < €.(b) If {n} converges, then there exists n E N such that for all € > 0, |Xn+1 − Xn| < €.(c) If {n} converges, then there exists € > 0 such that for all n € N, Xn+1 = n < €.

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Answered: #4 Short proofs and counterexamples,…

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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PROBLEM For any € > 0 show that the series 1 Σ exp| 12+€ n=1 converges almost everywhere. 2logn n Σπω) |k=1
In which of the following options, the statements given below and the general terms an that satisfy these statements are matched correctly? I: > 1 is divergent when > an is convergent an n=1 n=1 II: ) is divergent when >an is divergent an n=1 n=1 III: 2 is convergent when the sequence {an}- is divergent an n=1 1 M: an = 3 n' K: an = n? L: an = Vn (а) 1-М (b) I-L (c) I-M (d) I-L (е) 1-К II - K П-М II - L II - K II - M III - L III -K III - K III- M III - L
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