7. Let x₁ = a > 0 and Xn+1 = x + 1/x,, for n E N. Determine whether (x,) converges or diverges.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 74E
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7. Let x₁ = a > 0 and Xn+1 = x +1/x, forn € N. Determine whether (x₂) converges or diverges.
8. Let (a) be an increasing sequence, (b) be a decreasing sequence, and assume that an ≤ b, for
all n € N. Show that lim(a) ≤ lim(b), and thereby deduce the Nested Intervals Property 2.5.2
T
Transcribed Image Text:7. Let x₁ = a > 0 and Xn+1 = x +1/x, forn € N. Determine whether (x₂) converges or diverges. 8. Let (a) be an increasing sequence, (b) be a decreasing sequence, and assume that an ≤ b, for all n € N. Show that lim(a) ≤ lim(b), and thereby deduce the Nested Intervals Property 2.5.2 T
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