Using basic real analysis 1, solve the question 4. Prove or disprove by giving a counterexample:(a) If (xn) and (y) are divergent sequences then (xn +yn) diverges also.(b) If (xn) and (yn) are divergent sequences then (xn Yn) diverges also.(c) If (xn) and (z Yn) are convergent sequences then (yn) converges also.

A sequence is always convergent if it's limit is unique real number. A sequence is divergent if it…

Answered: 4. Prove or disprove by giving a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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4. Prove or disprove by giving a counterexample: (a) If (xn) and (Yn) are divergent sequences then (xn + Yn) diverges also. (b) If (xn) and (yn) are divergent sequences then (xn Yn) diverges also. (c) If (xn) and (¤n · Yn) are convergent sequences then (yn) converges also.