Sum of Positive Integers Calculator
Calculate the sum of consecutive positive integers quickly and easily. Enter the start and end numbers to find the sum using our intuitive online calculator.
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Calculation Steps:
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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.