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2. Suppose that the sequence {an} converges to a and that a < 1. Prove that the sequence {(an)"} converges to zero. (Hint: You need to use the fact that |a| < 1. You will need to point out in your proof how are using this.)

2. Suppose that the sequence {an} converges to a and that a < 1. Prove that the sequence {(an)"} converges to zero. (Hint: You need to use the fact that |a| < 1. You will need to point out in your proof how are using this.)

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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2. Suppose that the sequence {an} converges to a and that a < 1. Prove that the sequence {(an)"} converges to zero. (Hint: You need to use the fact that |a| < 1. You will need to point out in your proof how are using this.) 3. Let c be a number with e| < 1 Show that c] can be expressed as [c] = 1d where d > 0. Then use the Binomial Formula to show that || ≤nd ≤ for every index n
Transcribed Image Text:2. Suppose that the sequence {an} converges to a and that a < 1. Prove that the sequence {(an)"} converges to zero. (Hint: You need to use the fact that |a| < 1. You will need to point out in your proof how are using this.) 3. Let c be a number with e| < 1 Show that c] can be expressed as [c] = 1d where d > 0. Then use the Binomial Formula to show that || ≤nd ≤ for every index n
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