Python 程序查找算术级数之和

编写一个 Python 程序，通过实际示例查找算术级数（A.P. Series）的总和。

Python A.P. Series

算术级数是项的序列，其中下一项是通过在前一项上添加公差获得的。或者 A.P. 级数是一系列数字，其中任意两个连续数字的差始终相同。这个差称为公差。

算术级数计算背后的数学原理
A.P. 级数之和：Sn = n/2(2a + (n – 1) d)
A.P. 级数的 Tn 项：Tn = a + (n – 1) d

Python 程序查找算术级数示例之和

此 Python 程序允许用户输入第一个值、系列中的项目总数和公差。接下来，Python 找到算术级数的总和。

# Python Program to find Sum of Arithmetic Progression Series

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

total = (n * (2 * a + (n - 1) * d)) / 2
tn = a + (n - 1) * d

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

Python 程序计算算术级数之和示例 2

此 Python A.P. 总和程序与上面相同。在这里，我们使用 While 循环 来显示 A.P. 级数，这是可选的。

# Python Program to find Sum of Arithmetic Progression Series

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

total = (n * (2 * a + (n - 1) * d)) / 2
tn = a + (n - 1) * d
i = a
print("\nThe tn Term of Arithmetic Progression Series = " , tn)
print("The Sum of Arithmetic Progression Series : ")
while(i <= tn):
    if(i != tn):
        print("%d + " %i, end = " ")
    else:
        print("%d = %d" %(i, total))
    i = i + d

Python 算术级数总和输出

Please Enter First Number of an A.P Series: : 2
Please Enter the Total Numbers in this A.P Series: : 6
Please Enter the Common Difference : 4

The tn Term of Arithmetic Progression Series =  22
The Sum of Arithmetic Progression Series : 
2 +  6 +  10 +  14 +  18 +  22 = 72

Python 程序在没有数学公式的情况下计算算术级数之和

在此 Python 程序中，我们不使用任何数学公式。

# Python Program to find Sum of Arithmetic Progression Series

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

total = 0
value = a
print("Arithmetic Progression Series : ", end = " ")
for i in range(n):
    print("%d + " %value, end = " ")
    total = total + value
    value = value + d

print("\nThe Sum of Arithmetic Progression Series upto %d = %d " %(n, total))

Python 算术级数总和输出

Please Enter First Number of an A.P Series: : 1
Please Enter the Total Numbers in this A.P Series: : 4
Please Enter the Common Difference : 5
Arithmetic Progression Series :  1 +  6 +  11 +  16 +  
The Sum of Arithmetic Progression Series upto 4 = 34 

Python 程序使用函数计算算术级数之和

此 Python 算术级数总和与第一个示例相同。但是，我们使用 函数将逻辑分开了。

# Python Program to find Sum of Arithmetic Progression Series

def sumofAP(a, n, d):
    total = (n * (2 * a + (n - 1) * d)) / 2
    return total

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

total = sumofAP(a, n, d)
print("\nThe Sum of Arithmetic Progression Series = " , total)

Python 算术级数总和输出

Please Enter First Number of an A.P Series: : 2
Please Enter the Total Numbers in this A.P Series: : 5
Please Enter the Common Difference : 10

The Sum of Arithmetic Progression Series =  110.0