Math & Numbers

Series Convergence Tester (Ratio/Root/Integral/Comparison)

Numeric convergence tests for Σ aₙ: nth-term, ratio, root, p-series comparison, and integral test; alternating series classified by Leibniz with a sum estimate.

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Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/series-convergence-tester' \
  -H 'Content-Type: application/json' \
  -d '{"aNExpr":"1/n^2","decimalPlaces":4}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/series-convergence-tester

Parameters

Name	Type	Required	Description
aNExpr	text	Yes	The general term aₙ as an expression of n (n starts at 1). Supports + - * / ^, parentheses, and functions like exp, sin, cos, sqrt, ln. Alternating signs (e.g. cos(pi*n)) are detected.
decimalPlaces	number	No	—

Response format

Text result

JSON

{
  "result": "Processed text content",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-series-convergence-tester": {
      "name": "series-convergence-tester",
      "description": "Numeric convergence tests for Σ aₙ: nth-term, ratio, root, p-series comparison, and integral test; alternating series classified by Leibniz with a sum estimate.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=series-convergence-tester",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "series-convergence-tester",
    "arguments": {
  "aNExpr": "1/n^2",
  "decimalPlaces": 4
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

Browse tools Open tool

Name

Type

Required

Description

aNExpr

text

Yes

The general term aₙ as an expression of n (n starts at 1). Supports + - * / ^, parentheses, and functions like exp, sin, cos, sqrt, ln. Alternating signs (e.g. cos(pi*n)) are detected.

decimalPlaces

number

—

{ "mcpServers": { "elysiatools-series-convergence-tester": { "name": "series-convergence-tester", "description": "Numeric convergence tests for Σ aₙ: nth-term, ratio, root, p-series comparison, and integral test; alternating series classified by Leibniz with a sum estimate.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=series-convergence-tester", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }