Question

Use Theon's double sequence (Xn and Yn) method to find the first 10 rational approximations to square root of 11. You may use a computer program

Answer 1

Here is the short C++ program to do the above calculations:

#include <stdio.h>
#include<iostream>
using namespace std;
int main()
{
float x1=1, y=1, x2;
for(int i=1;i<=10;i++){
x2 = x1+y;
y = x2+10*x1;
float ans = y/x2;
cout<<x2<<" "<<y<<" "<<ans<<endl;
x1=x2;
}

return 0;
}