/* atk i - harjoitus 6, tehtävä 1 */

#include <stdio.h>
#include <math.h>

double exps(int n, double x);
double expw(int n, double x);

main()
{
    double x, summa1, summa2, tarkka;
    int n;

    printf("Lasken exp(x):n pot. sarjakehitelman n:teen\n"
           "asteeseen saakka. Anna n ja x:");

    scanf("%d%lf", &n, &x);

    summa1 = exps(n, x);
    summa2 = expw(n, x);
    tarkka = exp(x);

    printf("exps(x) = %.25f\n", summa1);
    printf("expw(x) = %.25f\n", summa2);
    printf("e^x = %.25f\n", tarkka);
    printf("S - e^x = %.25g\n", summa1 - tarkka);
}

double exps(int n, double x)
{
    int i;
    double s = 1, t = 1;

    for (i = 1; i <= n; i++)
    {
        t *= x / i;
        s += t;
    }

    return s;
}

double expw(int n, double x)
{
    int i;
    double s = 1, t = 1;

    i = 1;
    while (i <= n)
    {
        t *= x / i;
        s += t;
	i++;
    }

    return s;
}