Calculate Series Sum
About Convergent Series
A series is the sum of the terms in a sequence. For some sequences, the more terms are added, the closer the sum gets to some finite number. Such series are said to converge.
This tool approximates the sum of an infinite sequence by computing Σ(n=0, N)f(n) for some large N.
Some convergent series to try
| Series | JavaScript | Converges to |
|---|---|---|
| Geometric series (r=1/2) | 1 / Math.pow(2, n) |
2 |
| Geometric series (r=1/3) | 1 / Math.pow(3, n) |
1.5 |
| 1/n² series | 1 / Math.pow(n + 1, 2) |
π²/6 ≈ 1.645 |
| 1/n! series | 1 / factorial(n) |
e ≈ 2.718 |
| Alternating series | Math.pow(-1, n) / (n + 1) |
ln(2) ≈ 0.693 |
Note: For the factorial function, you'll need to define it first:
function factorial(n) { return n <= 1 ? 1 : n * factorial(n-1); }