curl --request POST \
  --url https://api.iotools.cloud/v1/tool/series-convergence-test-calculator \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "series": "p_series",
  "p": "2",
  "n0": "1",
  "numTerms": "5"
}
'

{
  "tool": "series-convergence-test-calculator",
  "tool_version": "1.0.2",
  "outputs": {
    "verdict": "Converges absolutely",
    "decisiveRule": "p-series test: Σ 1/n^p converges because p = 2 > 1.",
    "generalTerm": "aₙ = 1 / n^2",
    "divergenceTest": "lim aₙ = 0",
    "ratioTest": "L = 1 (inconclusive)",
    "rootTest": "L = 1 (inconclusive)",
    "partialSums": [
      {
        "n": "1",
        "an": "1",
        "sn-partial-sum": "1"
      },
      {
        "n": "2",
        "an": "0.25",
        "sn-partial-sum": "1.25"
      },
      {
        "n": "3",
        "an": "0.111111",
        "sn-partial-sum": "1.36111"
      },
      {
        "n": "4",
        "an": "0.0625",
        "sn-partial-sum": "1.42361"
      },
      {
        "n": "5",
        "an": "0.04",
        "sn-partial-sum": "1.46361"
      }
    ],
    "steps": "Series: p-series (Σ 1/nᵖ)\nGeneral term: aₙ = 1 / n^2\nStarting index n₀ = 1\n\nDivergence (nth-term) test: lim aₙ = 0\nRatio test: L = 1 (inconclusive)\nRoot test: L = 1 (inconclusive)\n\nVerdict: Converges absolutely\nReason: p-series test: Σ 1/n^p converges because p = 2 > 1.\n\nPartial sums:\n  S(1) = 1   (aₙ = 1)\n  S(2) = 1.25   (aₙ = 0.25)\n  S(3) = 1.36111   (aₙ = 0.111111)\n  S(4) = 1.42361   (aₙ = 0.0625)\n  S(5) = 1.46361   (aₙ = 0.04)"
  },
  "credits_used": 5,
  "credits_remaining": null
}