Python Program for Sum of first N even numbers

The sum of the first N even numbers is a mathematical operation where we add up the first N even numbers. In Python, there are multiple ways to calculate this sum. In this article, we will learn various approaches to finding the sum of the first N even numbers in Python.

Understanding the Problem

The first N even numbers form a sequence: 2, 4, 6, 8, 10, ... The mathematical formula for finding their sum is:

Sum = N * (N + 1)

Example: For N=5, the first 5 even numbers are: 2, 4, 6, 8, 10

Sum = 2 + 4 + 6 + 8 + 10 = 30

Using the Direct Formula

This is the most efficient approach using the formula Sum = N * (N + 1) ?

N = 5
sum_even = N * (N + 1)
print(f"The sum of the first {N} even numbers is: {sum_even}")

The sum of the first 5 even numbers is: 30

Time Complexity: O(1)

Using a Loop (Iterative Approach)

This approach uses a loop to iterate and calculate the sum by generating even numbers ?

N = 5  
sum_even = 0  
for i in range(1, N + 1):      
    sum_even += 2 * i  
print(f"The sum of the first {N} even numbers is: {sum_even}")

The sum of the first 5 even numbers is: 30

Time Complexity: O(N)

Using List Comprehension

Python provides a concise way using list comprehensions with the built-in sum() function ?

N = 5  
sum_even = sum([2 * i for i in range(1, N + 1)])
print(f"The sum of the first {N} even numbers is: {sum_even}") 

The sum of the first 5 even numbers is: 30

Time Complexity: O(N)

Using a Reusable Function

Creating a function makes the code modular and reusable ?

def sum_even_numbers(N):
    return N * (N + 1)

# Test the function
N = 5
result = sum_even_numbers(N)
print(f"The sum of the first {N} even numbers is: {result}")

# Test with different values
for n in [3, 7, 10]:
    print(f"N={n}: Sum = {sum_even_numbers(n)}")

The sum of the first 5 even numbers is: 30
N=3: Sum = 12
N=7: Sum = 56
N=10: Sum = 110

Comparison of Methods

Conclusion

The direct formula method N * (N + 1) is the most efficient with O(1) time complexity. Use the loop-based approach for educational purposes and list comprehension for Pythonic style, though both have O(N) complexity.