Sum of a Sequence
The sum of the first n terms of common sequences by closed formulas, with an exact result and steps.
n is a natural number up to 1,000,000. For powers of two up to 2000, for factorials up to 500.
This calculator finds the sum of the first n terms of common sequences using closed formulas. The result is exact even for very large n, and for small n the sum is checked by direct addition.
Main formulas
| Sum | Formula |
|---|---|
| 1 + 2 + … + n | n(n + 1) / 2 |
| 1² + 2² + … + n² | n(n + 1)(2n + 1) / 6 |
| 1³ + 2³ + … + n³ | (n(n + 1) / 2)² |
| 1 + 3 + … + (2n − 1) | n² |
| 1 + 2 + 4 + … + 2ⁿ⁻¹ | 2ⁿ − 1 |
Example. 1² + 2² + … + 10² = 10 · 11 · 21 / 6 = 385.
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