练习二十四：分数序列

问题：有个分数序列，2/1，3/2，5/3，8/5.。。，求数列前20向之和

思路：后一项分子是前一项得分母，后一项得分母是前一项分子和分母之和

方法一：

n = int(input("输入项："))
a,b,sum1 = 1.0,2.0,0.0
for i in range(n):
    sum1 += b/a
    a,b = b,a+b
print(sum1)

执行结果：

输入项：20
32.66026079864164

方法二：

from functools import reduce
a,b,s = 2.0,1.0,0.0
list1 = []
for i in range(20):
    list1.append(a/b)
    b,a = a,a+b
print(list1)
print(reduce(lambda x,y:x+y,list1))

执行结果：

[2.0, 1.5, 1.6666666666666667, 1.6, 1.625, 1.6153846153846154, 1.619047619047619, 1.6176470588235294, 1.6181818181818182, 1.6179775280898876, 1.6180555555555556, 1.6180257510729614, 1.6180371352785146, 1.618032786885246, 1.618034447821682, 1.6180338134001253, 1.618034055727554, 1.6180339631667064, 1.6180339985218033, 1.618033985017358]
32.66026079864164