Sum of Positive Integers Calculator

Easily calculate the sum of a sequence of positive integers. Enter the starting and ending numbers below!

Starting Number (n1):

Ending Number (n2):

Result:

Calculation Steps:

Understanding Sum of Positive Integers

The sum of positive integers, also known as the sum of natural numbers, is the result of adding a sequence of consecutive positive integers. For example, the sum of the first 5 positive integers (1, 2, 3, 4, 5) is 1 + 2 + 3 + 4 + 5 = 15.

Formula for Sum of Integers

For a range of positive integers from n1 to n2, the sum (S) can be calculated using the formula derived from the arithmetic series sum formula. A simplified approach leverages the formula for the sum of the first n natural numbers, which is given by:

$$ S_n = rac{n(n+1)}{2} $$

To find the sum from n1 to n2, we calculate the sum of the first n2 integers and subtract the sum of the first n1 - 1 integers. This is expressed as:

$$ S = rac{n_2(n_2+1)}{2} - rac{(n_1-1)n_1}{2} $$

Example

Let's calculate the sum of positive integers from 1 to 10:

n1 = 1
n2 = 10
Using the formula: S = (10 * (10 + 1)) / 2 - ((1 - 1) * 1) / 2 = (10 * 11) / 2 - 0 = 110 / 2 = 55

Therefore, the sum of positive integers from 1 to 10 is 55.