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

Last update on April 19 2025 12:55:41 (UTC/GMT +8 hours)

9. Geometric Series Sum Using Recursion

Write a Python program to calculate the geometric sum up to 'n' terms.
Note : In mathematics, a geometric series is a series with a constant ratio between successive terms.

Sample Solution:

Python Code:

# Define a function named geometric_sum that calculates the geometric sum up to 'n' terms
def geometric_sum(n):
    # Check if 'n' equals 0, which is the base case for the geometric sum
    if n == 0:  # Corrected base case condition
        # If 'n' equals 0, return 1 as the geometric sum in this case is 1
        return 1
    else:
        # If 'n' is not 0, calculate the term in the geometric series (1 / 2^n) and add it to
        # the result of recursively calling the geometric_sum function with 'n - 1'
        return 1 / (pow(2, n)) + geometric_sum(n - 1)
# Print the result of calling the geometric_sum function with the input value 7
print(geometric_sum(7))
# Print the result of calling the geometric_sum function with the input value 4
print(geometric_sum(4))

Sample Output:

1.9921875                                                                                                     
1.9375

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to recursively compute the sum of a geometric series given the first term and common ratio for n terms.
Write a Python program to implement a recursive function that calculates the sum of a geometric progression with a constant ratio.
Write a Python program to compute the geometric sum using recursion and verify the result with the geometric series formula.
Write a Python program to implement recursion for the sum of a geometric series and handle cases where the common ratio is less than one.

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