UVA10056

思考

無窮等比級數求和公式

原理： $Sn=a+ar+a{r}^2+a{r}^3+...+a{r}^n$ $公比=r$ 第n項： $a_n=a{r}^{n-1}$

把S - S * r $S=a+ar+a{r}^2+...-rS=ar+a{r}^2+a{r}^3...$ 求出： $S=\frac{a}{1-r}$

程式碼

import java.util.Scanner;
 
public class main {
    public static void main(String[] args) {
        int num = 0;
        int r = 100;
        Scanner sc = new Scanner(System.in);
        num = sc.nextInt();
        for(int i = 0 ; i < num ; i++){
            int n_count = sc.nextInt();
            float percent = sc.nextFloat();
 
            int index = sc.nextInt();
                        if(percent == 0){
                System.out.println("0.0000");
                continue;
            }		
             float ans = (float) ((float)Math.pow(1-percent, index-1)*percent*(1-Math.pow(Math.pow(1-percent,n_count), r))/(1-Math.pow(1-percent,n_count)));
            System.out.printf("%.4f", ans);
            System.out.println();
        }
    }
}