1. Prove that the sequence diverges but it has a convergent subsequence: (-1)" 2+(-1)", (a) (b) X = (rn) = (cos(na/2)) wwww. (c) X (n+(-1)"n).
1. Prove that the sequence diverges but it has a convergent subsequence: (-1)" 2+(-1)", (a) (b) X = (rn) = (cos(na/2)) wwww. (c) X (n+(-1)"n).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 65E
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![**Problem 1:** Prove that the sequence diverges but it has a convergent subsequence:
(a) \[ \left( \frac{(-1)^n}{2 + (-1)^n} \right) \]
(b) \( X = (x_n) = (\cos(n\pi/2)) \)
(c) \( X = (n + (-1)^{r_n}) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5203d42-0da6-4b1b-a1a9-5b37798d2cd6%2Ff97c2ac6-aa86-4640-812f-05fdc36b409d%2Fyhlr9jc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 1:** Prove that the sequence diverges but it has a convergent subsequence:
(a) \[ \left( \frac{(-1)^n}{2 + (-1)^n} \right) \]
(b) \( X = (x_n) = (\cos(n\pi/2)) \)
(c) \( X = (n + (-1)^{r_n}) \)
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