【详解】使用java解决-有一分数序列：2/1，3/2，5/3，8/5，13/8，21/13…求出这个数列的前20项之和。

public class FractionSequenceSum {
    public static void main(String[] args) {
        int n = 20; // 前20项
        double sum = 0.0;

        // 初始化分子和分母
        long numerator = 2;
        long denominator = 1;

        for (int i = 0; i < n; i++) {
            // 计算当前项的值
            double term = (double) numerator / denominator;
            sum += term;

            // 更新分子和分母
            long nextNumerator = numerator + denominator;
            denominator = numerator;
            numerator = nextNumerator;
        }

        System.out.println("前20项之和: " + sum);
    }
}

前20项之和: 32.6602693877551

public class FractionSequenceSum {
    public static void main(String[] args) {
        // 初始化第一个分数的分子和分母
        long numerator = 2; // 分子
        long denominator = 1; // 分母
        
        double sum = 0.0; // 存储总和

        for (int i = 0; i < 20; i++) {
            // 计算当前分数的值，并加到总和中
            double currentFraction = (double) numerator / denominator;
            sum += currentFraction;

            // 更新分子和分母为下一个分数的值
            long nextNumerator = numerator + denominator;
            denominator = numerator;
            numerator = nextNumerator;
        }

        System.out.printf("The sum of the first 20 terms is: %.15f\n", sum);
    }
}

The sum of the first 20 terms is: 32.660260798626503

import java.math.BigInteger;

public class FractionSequenceSum {
    public static void main(String[] args) {
        // 初始化第一项
        BigInteger a = BigInteger.valueOf(2); // 分子
        BigInteger b = BigInteger.valueOf(1); // 分母
        
        // 用于存储总和
        BigInteger sumNumerator = BigInteger.ZERO; // 总和的分子
        BigInteger sumDenominator = BigInteger.ONE; // 总和的分母

        for (int i = 0; i < 20; i++) {
            // 计算当前项的值
            BigInteger currentNumerator = a;
            BigInteger currentDenominator = b;

            // 将当前项加到总和中
            sumNumerator = sumNumerator.multiply(currentDenominator).add(sumDenominator.multiply(currentNumerator));
            sumDenominator = sumDenominator.multiply(currentDenominator);

            // 计算下一项
            BigInteger nextA = a.add(b);
            BigInteger nextB = a;
            a = nextA;
            b = nextB;
        }

        // 简化最终的总和
        BigInteger gcd = sumNumerator.gcd(sumDenominator);
        sumNumerator = sumNumerator.divide(gcd);
        sumDenominator = sumDenominator.divide(gcd);

        // 输出结果
        System.out.println("The sum of the first 20 terms is: " + sumNumerator + "/" + sumDenominator);
    }
}