relations: = 2: = 1. onvergent, one is

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 52E
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how to solve the attached qusetion without using limits

Three sequences are given by the recurrence relations:
12
(i)
Un+1
Vn+1 =
Wn+1
+1, where ₁ = 5;
1 (3v, 2²
4
-2v,, -8), when
2v₁
where v₁ = 2;
= w₁² - 2w₁ +3, where w₁ = 1.
Show that one of these sequences is convergent, one is
divergent and one is periodic.
Transcribed Image Text:Three sequences are given by the recurrence relations: 12 (i) Un+1 Vn+1 = Wn+1 +1, where ₁ = 5; 1 (3v, 2² 4 -2v,, -8), when 2v₁ where v₁ = 2; = w₁² - 2w₁ +3, where w₁ = 1. Show that one of these sequences is convergent, one is divergent and one is periodic.
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