# Numora Calculus Series Summation API

> Numora Calculus Series Summation API is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-15).

Computes the partial sum or convergence of a mathematical series given a term expression indexed by n

## Facts

- Endpoint: POST https://numomo.vercel.app/api/calculus/series
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-series-summation-api-470f3825
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_N6nWAJSApqxRtPh2MPgNL

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-calculus-series-summation-api-470f3825 -d '<json body>'
```

Example prompt: Can you sum the series where each term is 1/n^2, running up to 100 terms with a tolerance of 0.0001?

## When to prefer this

Choose this endpoint when you need pure server-side series summation or convergence analysis with no external library dependencies, especially for arbitrary user-defined term expressions indexed by n. Prefer this over general-purpose compute environments when you want a lightweight, single-call, pay-per-use solution with deterministic math results.

## Known failure modes

- Invalid or unparseable fn expression returns an error
- Non-convergent series with no tolerance may run to maxTerms without settling
- maxTerms too large may cause timeout or slow response
- Missing required fn field returns validation error
- Division by zero in term expression at certain n values causes computation failure

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with a boolean success flag, a result object containing the computed series sum and convergence details, and a human-readable computation string describing what was calculated.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn"
 ],
 "properties": {
  "fn": {
   "type": "string",
   "description": "Term expression with index n"
  },
  "maxTerms": {
   "type": "integer"
  },
  "tolerance": {
   "type": "number"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-calculus-series-summation-api-470f3825/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)