curl --request POST \
  --url https://api.iotools.cloud/v1/tool/infinite-series-sum-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "series": "geometric",
  "a": "1",
  "r": "0.5",
  "n0": "1",
  "numTerms": "5"
}
'

{
  "tool": "infinite-series-sum-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "converges": "Converges",
    "exactSum": "1·0.5^1 / (1 - 0.5)",
    "numericSum": "1",
    "formula": "S = a·rⁿ⁰ / (1 - r)",
    "reason": "|r| = 0.5 < 1, so the geometric series converges.",
    "partialSums": [
      {
        "n": "1",
        "an": "0.5",
        "sn-partial-sum": "0.5"
      },
      {
        "n": "2",
        "an": "0.25",
        "sn-partial-sum": "0.75"
      },
      {
        "n": "3",
        "an": "0.125",
        "sn-partial-sum": "0.875"
      },
      {
        "n": "4",
        "an": "0.0625",
        "sn-partial-sum": "0.9375"
      },
      {
        "n": "5",
        "an": "0.03125",
        "sn-partial-sum": "0.96875"
      }
    ],
    "steps": "Series: Geometric series (Σ a·rⁿ)\nConvergence: Converges\nReason: |r| = 0.5 < 1, so the geometric series converges.\nFormula: S = a·rⁿ⁰ / (1 - r)\nExact sum: 1·0.5^1 / (1 - 0.5)\nNumeric sum: 1\n\nPartial sums:\n  S(1) = 0.5   (aₙ = 0.5)\n  S(2) = 0.75   (aₙ = 0.25)\n  S(3) = 0.875   (aₙ = 0.125)\n  S(4) = 0.9375   (aₙ = 0.0625)\n  S(5) = 0.96875   (aₙ = 0.03125)"
  },
  "credits_used": 5,
  "credits_remaining": null
}