Let ƒ : [−1,1] → R be a continuous function. Prove that the sequence (n) defined inductively by Xn 1 2n 1+|xn| Xn+1 = Xn+ ƒ( x₁ = 0, converges. You may use theorems from the lecture as long as you state them explicitly.
Let ƒ : [−1,1] → R be a continuous function. Prove that the sequence (n) defined inductively by Xn 1 2n 1+|xn| Xn+1 = Xn+ ƒ( x₁ = 0, converges. You may use theorems from the lecture as long as you state them explicitly.
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 33E
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