Consider the series Xn+1 = Xn / 2 + 98 Xn, X0 = 0.5 obtained from the Newton-Raphson method. The series converges to

Question

Can any1 solve this pls

options:

A)1.5 B)

sqrt(2)

C)1.6

D)1.4

Answer 1

There is a printing mistake in the question,

Consider the series xn+1=xn/2+9/8xn,x0=0.5 obtained from the Newton-Raphson method. The series converges to
(A) 1.5 (B) √ 2(C) 1.6 (D) 1.4

Sol : Let us see which function's root is found using given series. We know that, according to Newton-Raphson method,

xn+1=xn−f(xn)/f′(xn)

So we try to bring given equation in above form. Given equation is :

xn+1=xn/2+9/8xn=xn−xn/2+9/8xn=xn−(4xn^2−9)/8xn

So clearly f(x)=4x^2−9. We know its roots are ±3/2=±1.5, but if we start from x0=0.5, according to equation, we cannot get negative value at any time, so answer is 1.5 i.e. option (A) is correct.