Sum of Series Calculator
The sum of series calculator helps you find the sum of an arithmetic or geometric series. Using this tool, you can also find the sum of an infinite geometric series.
Term 1039,366
Sum of the first 1059,048
Common ratio3
Sum to infinitydivergesneeds |r| < 1 to converge
Behaviourgrows without bound
Terms
| n | Term |
|---|---|
| 1 | 2 |
| 2 | 6 |
| 3 | 18 |
| 4 | 54 |
| 5 | 162 |
| 6 | 486 |
| 7 | 1,458 |
| 8 | 4,374 |
| 9 | 13,122 |
| 10 | 39,366 |
The formula
aₙ = a₁rⁿ⁻¹, Sₙ = a₁(1 − rⁿ) ÷ (1 − r)
Convergence depends only on r
An infinite geometric series converges exactly when |r| < 1, and then sums to a₁ ÷ (1 − r). That is why 1 + ½ + ¼ + ⅛ + … equals exactly 2, and why 0.999… equals exactly 1 — it is the geometric series with a₁ = 0.9 and r = 0.1.