Program to Calculate Sum of Series 1³+2³+3³+….+n³

Python Program to Calculate Sum of Series 1³+2³+3³+….+n³

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In the previous article, we have discussed Python Program to Find Isosceles Triangle Area
The general mathematical formula to calculate the sum of cubes of a series  =  ( n (n+1) / 6)²

where n= nth term of a series.

Given the nth term of a series and the task is to calculate the sum of the cubes of a series.

Math Module :

Python’s math module is a built-in module. By importing this module, we can perform mathematical computations.

Numerous mathematical operations like ceil( ),floor( ),factorial( ),mod( ),value of pi ,…..etc .can be computed with the help of math module.

math.pow() :

The math. pow() method returns the value of x to the power of y.

It throws a ValueError if x is negative and y is not an integer.

Both arguments are converted to floats by this method.

Note: Using math.pow(1.0,x) or math.pow(x,0.0) always returns 1.0.

Examples:

Example1:

Input:

Given n value = 13

Output:

The sum of cubes of a series with the given n value[ 13 ] = 8281.0

Example2:

Input:

Given n value = 6

Output:

The sum of cubes of a series with the given n value[ 6 ] = 441.0

Program to Calculate Sum of Series 1³+2³+3³+….+n³

Below are the ways to calculate the sum of the cubes of a given series.

Method #1: Using Mathematical Formula (Static Input)

Approach:

  • Import math module using the import keyword.
  • Give the nth term of a series () as static input and store it in a variable.
  • Calculate the sum of cubes of a series with a given nth term using the above mathematical formula and math.pow() function.
  • Store it in another variable.
  • Print the sum of cubes of a given series with the given n value.
  • The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Give the nth term of a series as static input and store it in a variable.
num = 10
# Calculate the sum of cubes of a series with a given nth term using the above
# mathematical formula and math.pow() function. 
# Store it in another variable.
cube_sum = math.pow((num * (num + 1)) / 2, 2)
# Print the sum of cubes of a given series with the given n value.
print(
    "The sum of cubes of a series with the given n value[", num, "] =", cube_sum)

Output:

The sum of cubes of a series with the given n value[ 10 ] = 3025.0

Method #2: Using Mathematical Formula (User Input)

Approach:

  • Import math module using the import keyword.
  • Give the nth term of a series as user input using the int(input()) function and store it in a variable.
  • Calculate the sum of cubes of a series with a given nth term using the above mathematical formula and math.pow() function.
  • Store it in another variable.
  • Print the sum of cubes of a given series with the given n value.
  • The Exit of the Program.

Below is the implementation:

# Import math module using the import keyword.
import math
# Give the nth term of a series as user input using the int(input()) function and store it in a variable.
num = int(input("Enter some random variable = "))
# Calculate the sum of cubes of a series with a given nth term using the above
# mathematical formula and math.pow() function. 
# Store it in another variable.
cube_sum = math.pow((num * (num + 1)) / 2, 2)
# Print the sum of cubes of a given series with the given n value.
print(
    "The sum of cubes of a series with the given n value[", num, "] =", cube_sum)

Output:

Enter some random variable = 8
The sum of cubes of a series with the given n value[ 8 ] = 1296.0

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