Sum of Positive Integers Calculator

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:

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:

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.