pthon: 数列sequence of number

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# encoding: utf-8 # 版权所有 2024 涂聚文有限公司 # 许可信息查看：言語成了邀功盡責的功臣，還需要行爲每日來值班嗎 # 描述：  数列： sequence of number # Author    : geovindu,Geovin Du 涂聚文. # IDE       : PyCharm 2024.3 python 3.11 # os        : windows 10 # database  : mysql 9.0 sql server 2019, poostgreSQL 17.0 oracle21C # Datetime  : 2024/12/28 8:12 # User      : geovindu # Product   : PyCharm # Project   : Pysimple # File      : mathdemo.py # explain   : 学习   import math import sys import matplotlib.pyplot as plt import numpy as np   def arithmeticSequence(start, step, length):     """     等差数列（arithmetic sequence）,生成    定义：等差数列是一种数列，其中任意两个相邻项的差是一个常数，这个常数被称为公差。设等差数列的首项为a 1 ，公差为d，则数列的通项公式为：a n =a 1 +(n−1)d     :param start: a1     :param step: d     :param length: n     :return:     """     return [start + step * i for i in range(length)]   def arithmeticsequence(a1, d, n):     """     等差数列（arithmetic sequence）,生成     :param a1:     :param d:     :param n:     :return:     """     return [a1 + (i * d) for i in range(n)]   def arithmeticsum(a1, d, n):     """     求和  Arithmetic Sequence     :param a1:     :param d:     :param n:     :return:     """     return (n / 2) * (2 * a1 + (n - 1) * d)       def geometricSequence(start, ratio, length):     """      等比数列（geometric sequence）生成     :param start:     :param ratio:     :param length:     :return:     """     return [start * ratio for i in range(length)]   def geometricsequence(a1, r, n):     """     等比数列（geometric sequence） 生成     :param a1:     :param r:     :param n:     :return:     """     return [a1 * (r ** i) for i in range(n)]   def geometricsum(a1, r, n):     """       :param a1:     :param r:     :param n:     :return:     """     if r == 1:         return a1 * n     return a1 * (1 - r ** n) / (1 - r)     def infinitegeometricsum(a1, r):     """       :param a1:     :param r:     :return:     """     if abs(r) >= 1:         return float('inf')  # or raise an exception     return a1 / (1 - r)   #Harmonic Sequence #Formula: an= 1 / (a1 + (n−1) * d) # 生成调和级数并计算其元素总和的函数 # 通过迭代实现 n = 5 AP = [0] * (n + 5)     def generateAP(a, d, n):     """       :param a:     :param d:     :param n:     :return:     """       sum = 0     for i in range(1, n + 1):           # HP = 1/AP         # In AP, ith term is calculated         # by a+(i-1)d;         AP[i] = (a + (i - 1) * d)           # Calculating the sum.         sum += float(1) / float((a + (i - 1) * d))     return sum   # Function that uses riemann sum method to calculate # the approximate sum of HP in O(1) time complexity     def sumApproximation(a, d, n):     """       :param a:     :param d:     :param n:     :return:     """     return math.log((2 * a + (2 * n - 1) * d) /                     (2 * a - d)) / d       #生成一个从1开始，公差为2，长度为10的等差数列 arithmeticseq = arithmeticSequence(1, 2, 10) print(arithmeticseq)  # 输出: [1, 3, 5, 7, 9, 11, 13, 15, 17, 19] #生成一个从1开始，公比为2，长度为10的等比数列 geometricseq = geometricSequence(1, 2, 10) print(geometricseq)  # 输出: [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]     # a = 12 d = 12 #n = 5;   # 根据上述数据生成 AP sum = generateAP(a, d, n)   #根据生成的 AP 产生 HP print("Harmonic Progression :") for i in range(1, n + 1):     print("1 /", AP[i], end=" ") print("") str1 = "" str1 = str1 + str(sum) str1 = str1[0:4]   print("Sum of the generated harmonic",       "progression :", str1) sum = sumApproximation(a, d, n)   str1 = "" str1 = str1 + str(sum) str1 = str1[0:4] print("Sum of the generated harmonic",       "progression using approximation :", str1)       arrayexample = np.arange(1, 11) squaresarray= [  1  , 4  , 9  ,16 , 25 , 36 , 49 , 64 , 81, 100] #可视化数列 plt.plot(arrayexample, squaresarray) plt.xlabel('Number') plt.ylabel('Square') plt.title('Number vs Square') plt.show()