Sum of series calculator (numbers, squares, cubes)
Pick the series and set the start and end to get the total at once, such as 1 + 2 up to 100. The math uses exact whole numbers with no rounding.
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How to use it
- Enter series, from and to.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Σk = n(n + 1) ÷ 2, Σk² = n(n + 1)(2n + 1) ÷ 6, Σk³ = [n(n + 1) ÷ 2]². The sum from a to b = S(b) - S(a - 1).
Example
Inputs: Series = Numbers: 1 + 2 + 3, From = 1, To = 100. Result: Sum: 5,050; Number of terms: 100.
Limits and caveats
- Start and end are whole numbers from 0 to one billion.
- For a step other than 1, use the arithmetic sequence calculator.
Questions about this tool
What is the sum of 1 to 100?
5050, from 100 × 101 ÷ 2.
What is the sum of the squares from 1 to 10?
385, from 10 × 11 × 21 ÷ 6.
Why is the sum of cubes a square?
It is a known identity: the sum of the cubes from 1 to n equals the square of the sum of 1 to n. Up to 10 that gives 3025 = 55².