B2. (a) Explain in detail what it means to say that a real sequence (an) is bounded.(b) Prove that every convergent sequence is bounded.(c) Prove that the sum of two bounded sequences is bounded.(d) Explain in detail what it means to say that a real sequence (an) diverges to ∞.(e) Suppose that the sequence (an) is bounded and the sequence (bn) diverges to .Prove that the sequence (an + bn) also diverges to ∞.

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Answered: B2. (a) Explain in detail what it means…

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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B2. (a) Explain in detail what it means to say that a real sequence (an) is bounded. (b) Prove that every convergent sequence is bounded. (c) Prove that the sum of two bounded sequences is bounded.