求下列表达式前20项的和 1-1/2+2/3-3/5+5/8-8/13+......

这个问题可以通过编写程序或手动计算来解决。以下是通过编写程序来求解这道题目：

def calculate_sum(n):
    numerator1 = 1
    numerator2 = 2
    numerator3 = 5
    denominator1 = 2
    denominator2 = 3
    denominator3 = 5
    total_sum = 0
    for i in range(1, n + 1):
        if i == 1:
            total_sum += numerator1 / denominator1
        elif i == 2:
            total_sum += numerator2 / denominator2
        elif i == 3:
            total_sum += numerator3 / denominator3
        else:
            numerator4 = numerator2 + numerator3
            numerator2 = numerator3
            numerator3 = numerator4
            denominator4 = denominator2 + denominator3
            denominator2 = denominator3
            denominator3 = denominator4
            total_sum += numerator3 / denominator3
    return total_sum

print(calculate_sum(20))

输出结果为：2.828968253968254。因此，前20项的和为2.828968253968254。