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If 0 < r < 1 and {n} is a sequence with the property |xnxn+1| < pn for n = 1,2,3,, then does {n}=1 converge or diverge? Prove your assertions.

If 0 < r < 1 and {n} is a sequence with the property |xnxn+1| < pn for n = 1,2,3,, then does {n}=1 converge or diverge? Prove your assertions.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 1E
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If 0 < r < 1 and {n} is a sequence with the property |xnxn+1| < pn for n = 1,2,3,, then does {n}=1 converge or diverge? Prove your assertions.
Transcribed Image Text:If 0 < r < 1 and {n} is a sequence with the property |xnxn+1| < pn for n = 1,2,3,, then does {n}=1 converge or diverge? Prove your assertions.
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