Define a sequence by recursion An + an+1 an+2 = with initial conditions aj = ì, a2 = µ where 1, u E R. Prove that the sequence converges. Hint: Use the Cauchy criterion. Perhaps it helps to picture the sequence in terms of cutting intervals in half.

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 73E
Question
Define a sequence by recursion
аn + an+1
An+2 =
with initial conditions
aj = ì, a2 = µ
where 1, u E R. Prove that the sequence converges.
Hint: Use the Cauchy criterion. Perhaps it helps to picture the sequence in terms of cutting intervals in
half.
Transcribed Image Text:Define a sequence by recursion аn + an+1 An+2 = with initial conditions aj = ì, a2 = µ where 1, u E R. Prove that the sequence converges. Hint: Use the Cauchy criterion. Perhaps it helps to picture the sequence in terms of cutting intervals in half.
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