Python Data Structures and Algorithms - Recursion: Calculate the harmonic sum

Last update on April 19 2025 12:56:13 (UTC/GMT +8 hours)

8. Harmonic Series Sum Using Recursion

Write a Python program to calculate the sum of harmonic series upto n terms.

Note: The harmonic sum is the sum of reciprocals of the positive integers.

Example:

harmonic series

Sample Solution:-

Python Code:

# Define a function named harmonic_sum that calculates the harmonic sum up to 'n' terms
def harmonic_sum(n):
    # Check if 'n' is less than 2 (base case for the harmonic sum)
    if n < 2:
        # If 'n' is less than 2, return 1 (base case value for the harmonic sum)
        return 1
    else:
        # If 'n' is greater than or equal to 2, calculate the reciprocal of 'n'
        # and add it to the result of recursively calling the harmonic_sum function with 'n - 1'
        return 1 / n + harmonic_sum(n - 1)

# Print the result of calling the harmonic_sum function with the input value 7
print(harmonic_sum(7))

# Print the result of calling the harmonic_sum function with the input value 4
print(harmonic_sum(4))

Sample Output:

2.5928571428571425                                                                                            
2.083333333333333

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to recursively calculate the sum of the harmonic series up to n terms.
Write a Python program to implement a recursive function that computes 1 + 1/2 + 1/3 + ... + 1/n.
Write a Python program to use recursion to sum the reciprocals of the first n positive integers.
Write a Python program to calculate the harmonic sum recursively and compare the result with an iterative loop version.

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Previous: Write a Python program to calculate the sum of the positive integers of n+(n-2)+(n-4)... (until n-x =< 0).
Next: Write a Python program to calculate the geometric sum of n-1.

Python Code Editor:

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