## Question

###### 17. Fix & > 1. Take x > 4, and define Jkvini; 66 } '72 & +xn a-x Xn+[ = =Xn + T+xn T+x (a) Prove that x1 >xa>xs> (6) Prove that Xz <x <xs < (c) Prove that lim x = Va_ (d) Compare the rapidity of convergence of this process with the one described in Exercise 16. 18. Replace the recursion formula of Exercise 16 byXn+1P_ Xn + X;p+1 pwhere p is a fixed positive integer, and describe the behavior of the resulting sequences {xa}:

17. Fix & > 1. Take x > 4, and define Jkvini; 66 } '72 & +xn a-x Xn+[ = =Xn + T+xn T+x (a) Prove that x1 >xa>xs> (6) Prove that Xz <x <xs < (c) Prove that lim x = Va_ (d) Compare the rapidity of convergence of this process with the one described in Exercise 16. 18. Replace the recursion formula of Exercise 16 by Xn+1 P_ Xn + X;p+1 p where p is a fixed positive integer, and describe the behavior of the resulting sequences {xa}:

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