Python 程序查找等比数列之和

编写一个Python程序来查找等比数列（G.P. Series）之和，并附带实际示例。

等比数列是指一系列元素，其中下一项是通过将公比乘以前一项获得的。或者说，等比数列是一系列数字，其中任何连续数字（项）的公比始终相同。

等比数列之和背后的数学公式。
Sn = a(rⁿ) / (1- r)
Tn = ar^(n-1)

Python 程序查找等比数列之和示例

此 Python 程序允许用户输入第一个值、系列中的项目总数以及公比。接下来，它查找等比数列的和。

# 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)

不使用数学公式查找等比数列之和的程序

在此 Python 程序中，我们不使用任何数学公式。

# 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)

等比数列之和输出

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

Python 程序使用函数计算等比数列之和

此等比数列程序与第一个示例相同。但是，在此 Python 程序中，我们使用函数分离了逻辑。

# 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)

等比数列之和输出

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