/* error_cancellation1.c
桁落ち
[1 / n - 1 / (n + 1)] * (n * (n + 1)) = 1 のはずが ...
*/

#include<stdio.h>

int main()
{
    int n, i;
    float x, y, z, w;
    n = 10;
    for(i = 0; i < 8; i++){
        x = 1.0 / n;
        y = 1.0 / (n + 1);
        z = x - y;
        w = z *  (n * (n + 1.0));
        printf("n = %9d のとき [1/n-1/(n+1)]*(n*(n+1)) = %f\n", n, w);
        n *= 10;
    }
}

/*

n =        10 のとき [1/n-1/(n+1)]*(n*(n+1)) = 1.000000
n =       100 のとき [1/n-1/(n+1)]*(n*(n+1)) = 0.999999
n =      1000 のとき [1/n-1/(n+1)]*(n*(n+1)) = 1.000075
n =     10000 のとき [1/n-1/(n+1)]*(n*(n+1)) = 0.999817
n =    100000 のとき [1/n-1/(n+1)]*(n*(n+1)) = 1.000454
n =   1000000 のとき [1/n-1/(n+1)]*(n*(n+1)) = 1.023183
n =  10000000 のとき [1/n-1/(n+1)]*(n*(n+1)) = 1.421086
n = 100000000 のとき [1/n-1/(n+1)]*(n*(n+1)) = 0.000000

*/