Compute Series with Radical Differences and Algebraic Denominator

Program Overview

This Python program reads an integer n and computes the result of the following series:
∑ [(√(k + 1) - √k) / √(k² + k)] for k from 2 to n
It uses math.sqrt for accurate computation of square roots.

Python Code:

import math

def compute_series(n: int) -> float:
    total = 0.0
    for k in range(2, n + 1):
        numerator = math.sqrt(k + 1) - math.sqrt(k)
        denominator = math.sqrt(k**2 + k)
        total += numerator / denominator
    return total

# Read input from user
n = int(input("Enter value for n: "))
result = compute_series(n)
print(f"Series result is: {result:.6f}")

Sample Output (input: n = 4):

Series result is: 0.162278