Python 程序：計算等比數列和

寫一個 Python 程序，用實例求等比數列(G.P .級數)的和。

Python 通用編程系列

等比數列是一個元素序列，其中下一個項目通過乘以上一個項目的公約數而獲得。或者 G.P. Series 是一系列數字，其中任何連續數字(項目)的公共比率總是相同的。

G.P 系列之和
Sn = a(rn)/(1-r)
Tn = ar(n-1)背後的數學公式

Python 程序求等比數列和的例子

這個 Python 程序允許用戶輸入第一個值、一系列項目的總數和公共定額。接下來，它找到等比數列的和。

# Python Program to find Sum of Geometric Progression Series
import math

a = int(input("Please Enter First Number of an G.P Series: : "))
n = int(input("Please Enter the Total Numbers in this G.P Series: : "))
r = int(input("Please Enter the Common Ratio : "))

total = (a * (1 - math.pow(r, n ))) / (1- r)
tn = a * (math.pow(r, n - 1))

print("\nThe Sum of Geometric Progression Series = " , total)
print("The tn Term of Geometric Progression Series = " , tn)

不用數學公式求等比數列和的程序

在這個 Python 程序中，我們沒有使用任何數學公式。

# Python Program to find Sum of Geometric Progression Series

a = int(input("Please Enter First Number of an G.P Series: : "))
n = int(input("Please Enter the Total Numbers in this G.P Series: : "))
r = int(input("Please Enter the Common Ratio : "))

total = 0
value = a
print("\nG.P  Series :", end = " ")
for i in range(n):
    print("%d  " %value, end = " ")
    total = total + value
    value = value * r

print("\nThe Sum of Geometric Progression Series = " , total)

等比數列輸出的 Python 和

Please Enter First Number of an G.P Series: : 1
Please Enter the Total Numbers in this G.P Series: : 5
Please Enter the Common Ratio : 4

G.P  Series : 1   4   16   64   256   
The Sum of Geometric Progression Series =  341

用函數計算等比數列和的 Python 程序

這個 Python 等比數列程序與第一個示例相同。然而，在這個 Python 程序中，我們使用函數來分離邏輯。

# Python Program to find Sum of Geometric Progression Series
import math

def sumofGP(a, n, r):
    total = (a * (1 - math.pow(r, n ))) / (1- r)
    return total

a = int(input("Please Enter First Number of an G.P Series: : "))
n = int(input("Please Enter the Total Numbers in this G.P Series: : "))
r = int(input("Please Enter the Common Ratio : "))

total = sumofGP(a, n, r)
print("\nThe Sum of Geometric Progression Series = " , total)

寶潔系列輸出的 Python 和

Please Enter First Number of an G.P Series: : 2
Please Enter the Total Numbers in this G.P Series: : 6
Please Enter the Common Ratio : 3

The Sum of Geometric Progression Series =  728.0