# Infinite Series Sum Calculator API

> For the complete documentation index, see [llms.txt](/llms.txt).

Closed-form sums for classic infinite series: geometric, p-series, telescoping, alternating harmonic, Leibniz, Basel, e^x, and alternating p-series.

Use this endpoint to add the tool to your app, site, workflow, or agent without rebuilding formulas, validation, examples, and docs.

- Slug: `infinite-series-sum-calculator`
- Category: `math`
- Version: `2026-04-22`
- Credits per successful call: 1
- Starts on: free
- Max payload: 65536 bytes
- Privacy mode: `hash_only`
- Available on: free, starter, pro, business, scale
- Browser tool: https://miniwebtool.com/infinite-series-sum-calculator/

## Endpoint

`POST https://api.miniwebtool.com/v1/tools/infinite-series-sum-calculator/run`

## Request body

| Field | Type | Required | Description |
| --- | --- | --- | --- |
| `series_type` | `str` | no | geometric | p_series | telescoping | alt_harmonic | leibniz | basel | exp_x | alt_p Choices: geometric, p_series, telescoping, alt_harmonic, leibniz, basel, exp_x, alt_p |
| `a` | `float` | no | First term (geometric) |
| `r` | `float` | no | Common ratio (geometric) |
| `n_start` | `int` | no | Starting index (geometric) |
| `p` | `float` | no | Exponent (p_series / alt_p) |
| `k` | `int` | no | Gap k in 1/(n(n+k)) (telescoping) |
| `x` | `float` | no | Argument x (exp_x) |

## Example request

```json
{
  "series_type": "geometric",
  "a": 1,
  "r": 0.5
}
```

## cURL

```bash
curl -X POST https://api.miniwebtool.com/v1/tools/infinite-series-sum-calculator/run \
  -H 'Authorization: Bearer mwt_live_YOUR_KEY' \
  -H 'Content-Type: application/json' \
  -d '{"series_type":"geometric","a":1,"r":0.5}'
```

## Response envelope

```json
{
  "request_id": "01K...",
  "tool": "infinite-series-sum-calculator",
  "tool_version": "2026-04-22",
  "credits_used": 1,
  "result": {}
}
```

## Errors

Errors are RFC 7807 `application/problem+json`. Branch on `code`, not `title`.

## MCP

Agents can discover and call this tool through `https://api.miniwebtool.com/mcp` or `https://api.miniwebtool.com/v1/mcp` using MCP `tools/list` and `tools/call`.

## Frequently asked

### What does the Infinite Series Sum Calculator API do?

Closed-form sums for classic infinite series: geometric, p-series, telescoping, alternating harmonic, Leibniz, Basel, e^x, and alternating p-series. Use it to add this utility without rebuilding formulas, validation, examples, and documentation.

### How much does one call cost?

1 credit per successful call. Failed calls do not bill.

### What parameters are required?

Required fields: (none). Full schema at `https://api.miniwebtool.com/v1/openapi.json`.

### Is this deterministic?

Yes. Same input, same output. Tool version: 2026-04-22.