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1. Prove or give counterexample. (a) If (xn) and (Yn) diverge, then (an + Yn) diverges. (b) If (xn) and (Yn) diverge, then (xnYn) diverges. (c) If (xn) and (xn + Yn) converge, then (yn) converges.

1. Prove or give counterexample. (a) If (xn) and (Yn) diverge, then (an + Yn) diverges. (b) If (xn) and (Yn) diverge, then (xnYn) diverges. (c) If (xn) and (xn + Yn) converge, then (yn) converges.

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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1. Prove or give counterexample. (a) If \( (x_n) \) and \( (y_n) \) diverge, then \( (x_n + y_n) \) diverges. (b) If \( (x_n) \) and \( (y_n) \) diverge, then \( (x_n y_n) \) diverges. (c) If \( (x_n) \) and \( (x_n + y_n) \) converge, then \( (y_n) \) converges. (d) If \( (x_n) \) and \( (x_n y_n) \) converge, then \( (y_n) \) converges.
Transcribed Image Text:1. Prove or give counterexample. (a) If \( (x_n) \) and \( (y_n) \) diverge, then \( (x_n + y_n) \) diverges. (b) If \( (x_n) \) and \( (y_n) \) diverge, then \( (x_n y_n) \) diverges. (c) If \( (x_n) \) and \( (x_n + y_n) \) converge, then \( (y_n) \) converges. (d) If \( (x_n) \) and \( (x_n y_n) \) converge, then \( (y_n) \) converges.
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