java - 如何在java中编写1+1/2+1/3....+1/4999+1/5000？

Question

如何用java编写1+1/2+1/3....+1/4999+1/5000？ 我已经尝试过了，但没有成功。

public class Harmonic{
  public static void main(String[] args){
    double sum = 0;
    for(int i=1; i<=5000; i++){
      sum+=1/i;
    }
    System.out.println(sum);
  }
}

Answer 1

将数字从小到大相加将具有较低的舍入误差。如果以更高的精度比较结果，您会发现小到大更接近。

double sum = 0;
for (int i = 1; i <= 5000; i++) {
    sum += 1.0 / i;
}
System.out.println("From largest to smallest " + sum);

double sum2 = 0;
for (int i = 5000; i >= 1; i--) {
    sum2 += 1.0 / i;
}
System.out.println("From smallest to largest " + sum2);

BigDecimal sum3 = BigDecimal.ZERO;
for (int i = 5000; i >= 1; i--) {
    sum3 = sum3.add(BigDecimal.ONE.divide(BigDecimal.valueOf(i), 30, BigDecimal.ROUND_HALF_UP));
}
System.out.println("BigDecimal               " + sum3);

打印

From largest to smallest 9.094508852984404
From smallest to largest 9.09450885298443
BigDecimal               9.094508852984436967261245533401