Python Data Structures and Algorithms - Recursion: Sum of n+(n-2)+(n-4)...

Last update on March 27 2025 12:50:26 (UTC/GMT +8 hours)

7. Sum of Series n + (n-2) + (n-4) ... Using Recursion

Write a Python program to calculate the sum of the positive integers of n+(n-2)+(n-4)... (until n-x =< 0) using recursion.

Sample Solution:

Python Code:

# Define a function named sum_series that calculates the sum of a series of numbers
def sum_series(n):
    # Check if 'n' is less than 1 (base case for the series)
    if n < 1:
        # If 'n' is less than 1, return 0 (base case value for the sum)
        return 0
    else:
        # If 'n' is greater than or equal to 1, calculate the sum of 'n' and
        # recursively call the sum_series function with 'n - 2'
        return n + sum_series(n - 2)

# Print the result of calling the sum_series function with the input value 6
print(sum_series(6))

# Print the result of calling the sum_series function with the input value 10
print(sum_series(10))

Sample Output:

12                                                                                                            
30

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to recursively compute the sum of the series n, n-2, n-4, ... until the term is less than or equal to 0.
• Write a Python program to implement a recursive function that sums the series of positive integers decrementing by 2 at each step.
• Write a Python program to calculate the sum of the series n + (n-2) + ... using recursion and verify it with an iterative approach.
• Write a Python program to use recursion to sum a decreasing sequence starting from n with a step of 2, stopping when the term is non-positive.

Python Code Editor:

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