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Suppose that the sequence {an} converges to a and that la| < 1. Prove that the sequence {(an)"} converges to 0.

Suppose that the sequence {an} converges to a and that la| < 1. Prove that the sequence {(an)"} converges to 0.

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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7. Suppose that the sequence \((a_n)\) converges to \(a\) and that \(|a| < 1\). Prove that the sequence \((a_n)^n\) converges to 0.
Transcribed Image Text:7. Suppose that the sequence \((a_n)\) converges to \(a\) and that \(|a| < 1\). Prove that the sequence \((a_n)^n\) converges to 0.
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