#include <fstream.h>

//----------------------------------------------------------------------------------------------------------------------------

//     Truncation error demonstrated by numerrical approximation of Taylor series expansion

//      by Ching-Han Chen

//      2006-03-07

//-------------------------------------------------------------------------------------------------------------------------

void main()

{

    float x;

    x=1.0+0.1;

    cout<<x<<endl;

    x=1.0+0.1+(0.1*0.1)/(2.0*1.0);

    cout<<x<<endl;

    x=1.0+0.1+(0.1*0.1)/(2.0*1.0)+(0.1*0.1*0.1)/(3.0*2.0*1.0);

    cout<<x<<endl;

    x=1.0+0.1+(0.1*0.1)/(2.0*1.0)+(0.1*0.1*0.1)/(3.0*2.0*1.0)+(0.1*0.1*0.1*0.1)/(4.0*3.0*2.0*1.0);

    cout<<x<<endl;

    int i,j;

    float s1,s2;

    x=1.1;

    for(i=0;i<100;i++)

    {

        s1=s2=1;

        for(j=i+2;j>=1;j--)

        {

            s1=0.1*s1;

            s2=s2*j;

        }

        x=x+s1/s2;

    }

    cout<<x<<endl;

}