Question 11 of 13intermediate🔧 ApplyLong Answer4 marks

Write a program to find the sum of 1+ 1/8 + 1/27……1/n³, where n is the number input by the user.

Correct Answer

python #Program to find the sum of series 1 + 1/8 + 1/27 + ... + 1/n³ n = int(input("Enter the value of n: ")) sum1 = 0 for i in range(1, n + 1): sum1 = sum1 + 1/(i**3) print("The sum of the series is:", sum1)

Output:

Enter the value of n: 3 The sum of the series is: 1.162037037037037

In this program, the user inputs the value of n which determines how many terms of the series will be added. The series follows the pattern where each term is 1 divided by the cube of the term number (i³). A for loop iterates from 1 to n, and in each iteration, the term 1/i³ is calculated and added to the variable sum1 which stores the cumulative sum. Finally, the total sum is printed.

Exercise: PROGRAMMING EXERCISES | Q: 6
For More Understanding

Explanation

This question tests the student's understanding of loops and mathematical series computation. The series 1 + 1/8 + 1/27 + ... + 1/n³ can be expressed as Σ(1/i³) where i goes from 1 to n. The program uses a for loop with range(1, n+1) to iterate through each term, calculates 1/i³ using the exponentiation operator (**), and accumulates the sum. The context from Program 6-13 and Program 6-19 demonstrates similar patterns of using loops for summation and taking user input with int(input()).

Solution Steps

  1. Step 1: Accept integer input n from user using int(input())

  2. Step 2: Initialize sum1 = 0 to store the cumulative sum

  3. Step 3: Use for loop with range(1, n+1) to iterate through each term

  4. Step 4: Calculate each term as 1/(i**3) and add to sum1

  5. Step 5: Print the final sum after the loop completes

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