Requirements:
Factorial: It is also a term in mathematics; factorial refers to multiplying from 1 times 2 times 3 times 4 to the required number; when expressing factorial, use " !"To represent. For example, h factorial is expressed as h!; factorial is generally difficult to calculate because the products are very large.
Question: Find the sum of 1+2!+3!+...+20!
Implementation environment: python3
Editor:pycharm
Analysis: 1. The calculation of factorial is a troublesome part. Using recursive function is a better solution. First define a recursive function to implement the solution. factorial function.
def recursion(n): '定义递归函数实现求阶乘功能' if n==1: return 1 else: return n*recursion(n-1)
2. The idea of summing can be summed directly, or you can define a list to append the factorial results obtained by for traversal to the list, and then use the sum() function to sum.
sum_0=0 print("for循环直接调用递归函数求和".center(80,"*")) #显示效果明显 for i in range(1,21): sum_0 +=recursion(i) print(sum_0) 列表求和方案: list=[] #定义一个空的列表,将调用递归函数生成的阶乘值追加到列表 print("将1-20的阶乘写入列表,使用sum函数求和".center(80,"*")) #显示效果明显 for i in range(1,21): list.append(recursion(i))# 将调用递归函数生成的阶乘值追加到列表 print(sum(list)) #列表求和
Both can achieve their functions with the same number of lines of code.
Use knowledge points: recursive functions, for loops, range() functions, etc.
Complete source code and results:
#/usr/bin/env python #_*_coding:utf-8_*_ def recursion(n): '定义递归函数实现求阶乘功能' if n==1: return 1 else: return n*recursion(n-1) list=[] #定义一个空的列表,将调用递归函数生成的阶乘值追加到列表 print("将1-20的阶乘写入列表,使用sum函数求和".center(80,"*")) #显示效果明显 for i in range(1,21): list.append(recursion(i))# 将调用递归函数生成的阶乘值追加到列表 print(sum(list)) #列表求和 sum_0=0 print("for循环直接调用递归函数求和".center(80,"*")) #显示效果明显 for i in range(1,21): sum_0 +=recursion(i) print(sum_0) 结果: *****************************将1-20的阶乘写入列表,使用sum函数求和***************************** 2561327494111820313 ********************************for循环直接调用递归函数求和********************************* 2561327494111820313
It has been verified that both can achieve basic functions, but calculations with larger amounts of data have not been tested.
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