We consider the function \(f(x)=\frac{1}{1+x^2}\) and the series \(u_0=1\) and \(u_{n+1}=f(u_n)\)

Write a program that calculates and displays the successive terms of \(u_n\) until \(|u_{n+1}-u_n|\) is less than \(\epsilon=10^{-8}\).

#include <stdio.h>
#include <math.h>
#include <conio.h>
void main()
{
	double u,eps,ua,diff; int n;
	u=1.; eps=1.e-8; n=0;
	do
	{
		printf("u(%d)=%20.15lg\n",n,u);
		ua=u;
		u=1./(1.+u*u);
		n++;
		diff=fabs(u-ua);
	}while(diff>=eps);
	getch();
}