Python Program to Find Sum of Series 1+2+3+...+n

You can find the sum of the series 1+2+3+...+n in Python using the formula sum = n * (n + 1) // 2 or by looping from 1 to n and adding each number.

Examples

Input5

Output15

Input10

Output55

Input1

Output1

How to Think About It

To find the sum of numbers from 1 to n, think of adding all numbers one by one or use the shortcut formula that multiplies n by (n plus 1) and divides by 2. This formula works because the series is an arithmetic progression with a difference of 1.

Algorithm

1

Get the input number n.

2

Calculate the sum using the formula sum = n * (n + 1) // 2.

3

Print or return the sum.

Code

python

n = int(input('Enter a positive integer: '))
sum_series = n * (n + 1) // 2
print('Sum of series 1 to', n, 'is:', sum_series)

Output

Enter a positive integer: 5
Sum of series 1 to 5 is: 15

Dry Run

Let's trace the example where n=5 through the code.

1

Input

User enters n = 5

2

Calculate sum

sum_series = 5 * (5 + 1) // 2 = 5 * 6 // 2 = 30 // 2 = 15

3

Output

Print 'Sum of series 1 to 5 is: 15'

n	Calculation	sum_series
5	5 * (5 + 1) // 2	15

Why This Works

Step 1: Use of formula

The formula n * (n + 1) // 2 calculates the sum of the first n natural numbers quickly without looping.

Step 2: Integer division

Using // ensures the result is an integer since the sum of natural numbers is always whole.

Step 3: Input and output

The program takes input from the user and prints the sum clearly.

Alternative Approaches

Using a for loop

python

n = int(input('Enter a positive integer: '))
sum_series = 0
for i in range(1, n + 1):
    sum_series += i
print('Sum of series 1 to', n, 'is:', sum_series)

This method is easy to understand but slower for large n compared to the formula.

Using recursion

python

def sum_series(n):
    if n == 1:
        return 1
    else:
        return n + sum_series(n - 1)
n = int(input('Enter a positive integer: '))
print('Sum of series 1 to', n, 'is:', sum_series(n))

Recursion shows a different approach but can cause stack overflow for very large n.

Complexity: O(1) time, O(1) space

Time Complexity

Using the formula takes constant time because it performs only a few arithmetic operations regardless of n.

Space Complexity

The formula uses constant space as it stores only a few variables.

Which Approach is Fastest?

The formula method is fastest and most efficient compared to looping or recursion, which take O(n) time.

Approach	Time	Space	Best For
Formula	O(1)	O(1)	Fastest for any n
For loop	O(n)	O(1)	Easy to understand, small n
Recursion	O(n)	O(n)	Learning recursion, small n