Series Sum Calculator
First term (a)
Common diff (d)
Number of terms (n)
Series sum calculators find the total of all terms in arithmetic, geometric, or special mathematical series. They have applications in finance (annuities), physics, and pure mathematics.
- 1Arithmetic: Sₙ = n/2 × (2a + (n−1)d)
- 2Sum 1 to n: n(n+1)/2
- 3Sum of squares: n(n+1)(2n+1)/6
- 4Sum of cubes: [n(n+1)/2]²
1+2+3+...+100=100×101/2 = 5050 (Gauss method)
Arithmetic: a=1, d=2, n=10=Sum = 10/2×(2+18) = 100
| Series | Formula | Example (n=10) |
|---|---|---|
| 1+2+...+n | n(n+1)/2 | 55 |
| 1²+2²+...+n² | n(n+1)(2n+1)/6 | 385 |
| 1³+2³+...+n³ | [n(n+1)/2]² | 3025 |
| Arithmetic | n/2×(2a+(n-1)d | Varies |
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