{ x_(n+1) = 3 + [6/(3 + x_n)] } Beginning with a firs approximation of x_1 = 4, find the next 6 terms in the sequence: x_2, x_3, x_4, x_5, x_6, x_7. Also show how accurate the approximation is for |x_7 - sqrt 15| by giving { | x_7 - sqrt(15) | }
{ x_(n+1) = 3 + [6/(3 + x_n)] } Beginning with a firs approximation of x_1 = 4, find the next 6 terms in the sequence: x_2, x_3, x_4, x_5, x_6, x_7. Also show how accurate the approximation is for |x_7 - sqrt 15| by giving { | x_7 - sqrt(15) | }
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Consider the following sequence which can be used to approximate sqrt 15 , which is defined recursively by
{ x_(n+1) = 3 + [6/(3 + x_n)] }
Beginning with a firs approximation of x_1 = 4, find the next 6 terms in the sequence: x_2, x_3, x_4, x_5, x_6, x_7.
Also show how accurate the approximation is for |x_7 - sqrt 15| by giving
{ | x_7 - sqrt(15) | }
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