{
  "category": "Math and trigonometry functions",
  "display_name": "SERIESSUM",
  "entry_kind": "built_in_function",
  "eval_api": {
    "method": "POST",
    "url": "https://handbook.dnacalc.com/api/eval"
  },
  "function_id": "FUNC.SERIESSUM",
  "implementation_state": {
    "answer_bank": null,
    "detail": "Recorded: 7 workbook cells.",
    "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87",
    "in_catalogue": true,
    "state": "matches",
    "state_label": "Matches every recorded Excel answer",
    "summary": "Matches all 7 recorded answers",
    "workbook_corpus": {
      "cells": 7,
      "matched": 7
    }
  },
  "implementations": [
    {
      "commit": "9e1884369a678158dd82d3d74188daf986995e87",
      "flavour": "excel-compatibility-candidate",
      "language": "Rust",
      "name": "CalcFunc",
      "own_code": [
        "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/math.rs#L193-L208"
      ],
      "repository": "https://github.com/DnaCalc/DnaCalc",
      "shared_code": [],
      "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/math.rs#L193-L208",
      "state": "matches",
      "suite": null,
      "summary": "Matches all 7 recorded answers"
    }
  ],
  "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.SERIESSUM.json",
  "name": "SERIESSUM",
  "notes": [],
  "schema": "efh.function-reference/v1",
  "section_order": [
    "what-it-does",
    "try-it",
    "quirks",
    "how-to-implement",
    "version-differences",
    "alternatives"
  ],
  "sections": {
    "alternatives": "\n[SUMPRODUCT](FUNC.SUMPRODUCT.md) can combine explicit powers and coefficients; [POWER](FUNC.POWER.md) evaluates one term’s power. Horner evaluation is a mathematical alternative for polynomial series.\n\n\n",
    "how-to-implement": "\n1. Read numeric `x,n,m`, then the coefficient grid. Traverse coefficient cells in row order, retaining their positions.\n2. For zero-based coefficient index i, form exponent `e=n+i*m` with a binary64 multiplication followed by an addition.\n3. Obtain the internal runtime power `crt_pow(x,e)`. This is the current code’s leaf, not the public worksheet POWER wrapper.\n4. Multiply by coefficient `a_i`, then add the term to a binary64 accumulator initialized to zero. Preserve the term and sum order and apply worksheet result publication afterward.\n\nFor the first example, the accumulator visits one, seven, then fifteen. With a two-row coefficient array `{1,3;2,4}`, the same row traversal at x=2, n=0, m=1 gives `1+6+8+32=47`.\n\nHorner evaluation can avoid repeated powers for an ordinary polynomial. It can also change rounding, overflow and invalid-power behaviour. Treat it as a separate numerical implementation choice until compared; the series definition alone does not identify Excel’s internal power algorithm or all its storage stages.\n\n\n",
    "quirks": "\nMicrosoft documents `#VALUE!` for nonnumeric arguments. The current first-three-argument reader rejects logical values. Its coefficient grid accepts numeric cells, propagates a worksheet error and returns `#VALUE!` for other coefficient kinds; blank or text coefficients are not skipped as they can be in some aggregates.\n\nThe current graph evaluates a power before multiplying by its coefficient. A zero coefficient therefore does not erase an invalid power: the current route for `SERIESSUM(-1,0.5,1,{0})` reaches `#NUM!`. Negative bases and fractional exponents need the real power-domain policy. Overflow and underflow of terms can matter even when the mathematical sum would be finite.\n\n\n",
    "sources": "\n- [Microsoft: SERIESSUM function](https://support.microsoft.com/en-us/excel/functions/seriessum-function), opened 6 November 2026; syntax, documented argument rules and errors.\n- [DnaCalc implementation](https://github.com/DnaCalc/DnaCalc/blob/da3ecc4fb19a3a5529708c311d0e8f05688ac165/crates/calc-func/src/catalogue/math.rs); implementation steps and the limits identified in the text.\n\n",
    "try-it": "\n`=SERIESSUM(2,0,1,{1,3,2})` returns `15`:\n\n| Coefficient index | Exponent | Term |\n|---:|---:|---:|\n| 0 | 0 | `1*2^0=1` |\n| 1 | 1 | `3*2^1=6` |\n| 2 | 2 | `2*2^2=8` |\n\nChanging m to two uses exponents zero, two and four: `=SERIESSUM(2,0,2,{1,3,2})` returns `45`. The exponent step belongs to the powers, rather than changing the coefficient values.\n\n\n",
    "version-differences": "\nNo same-input comparison between named Excel builds is recorded for this function here. The documented behaviour below is not a measurement of every Excel release.\n\n\n",
    "what-it-does": "\n`SERIESSUM(x,n,m,coefficients)` adds terms `a_i*x^(n+i*m)`, starting with coefficient index i=0. N is the initial exponent and m the exponent step; the coefficient count determines the number of terms.\n\n\n"
  },
  "signature": {
    "display": "SERIESSUM(x, n, m, coefficients)",
    "parameters": [
      {
        "description": null,
        "name": "x",
        "optional": false,
        "repeats": false
      },
      {
        "description": null,
        "name": "n",
        "optional": false,
        "repeats": false
      },
      {
        "description": null,
        "name": "m",
        "optional": false,
        "repeats": false
      },
      {
        "description": null,
        "name": "coefficients",
        "optional": false,
        "repeats": false
      }
    ],
    "trailing_repeats": false
  },
  "sources": {
    "metadata": {
      "admission": {
        "label": "implemented",
        "reason": null
      },
      "arity": {
        "max": 4,
        "min": 4
      },
      "category": "Math and trigonometry functions",
      "classification": {
        "arg_preparation_profile": "RefsVisibleInAdapter",
        "coercion_lift_profile": "Custom",
        "determinism_class": "Deterministic",
        "error_collapse_profile": "None",
        "fec_dependency_profile": "RefOnly",
        "host_interaction_class": "None",
        "kernel_signature_class": "Custom",
        "rich_value_usage": "RichBlind",
        "surface_fec_dependency_profile": "RefOnly",
        "thread_safety_class": "SafePure",
        "volatility_class": "NonVolatile"
      },
      "descriptions": {
        "long": null,
        "short": "Sum of a power series with given coefficients",
        "short_source": "dna-calc-own"
      },
      "docs": {
        "english_description": "Returns the sum of a power series based on the formula",
        "microsoft_url": "https://support.microsoft.com/en-us/office/seriessum-function-a3ab25b5-1093-4f5b-b084-96c49087f637"
      },
      "entry_kind": "built_in_function",
      "localized_family_names": null,
      "localized_names": [
        {
          "locale": "ar-SA",
          "name": "SERIESSUM"
        },
        {
          "locale": "bg-BG",
          "name": "SERIESSUM"
        },
        {
          "locale": "cs-CZ",
          "name": "SERIESSUM"
        },
        {
          "locale": "da-DK",
          "name": "SERIESUM"
        },
        {
          "locale": "de-DE",
          "name": "SERIESSUM"
        },
        {
          "locale": "el-GR",
          "name": "SERIESSUM"
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        {
          "locale": "en-AU",
          "name": "SERIESSUM"
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          "locale": "en-GB",
          "name": "SERIESSUM"
        },
        {
          "locale": "en-US",
          "name": "SERIESSUM"
        },
        {
          "locale": "es-ES",
          "name": "SUMA.SERIES"
        },
        {
          "locale": "et-EE",
          "name": "SERIESSUM"
        },
        {
          "locale": "fi-FI",
          "name": "SARJA.SUMMA"
        },
        {
          "locale": "fr-FR",
          "name": "SOMME.SERIES*"
        },
        {
          "locale": "he-IL",
          "name": "SERIESSUM"
        },
        {
          "locale": "hr-HR",
          "name": "SERIESSUM"
        },
        {
          "locale": "hu-HU",
          "name": "SORÖSSZEG"
        },
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          "locale": "id-ID",
          "name": "SERIESSUM"
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          "name": "SERIESSUM"
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          "name": "SERIESSUM"
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          "locale": "lt-LT",
          "name": "SERIESSUM"
        },
        {
          "locale": "lv-LV",
          "name": "SERIESSUM"
        },
        {
          "locale": "nb-NO",
          "name": "SUMMER.REKKE"
        },
        {
          "locale": "nl-NL",
          "name": "SOM.MACHTREEKS"
        },
        {
          "locale": "pl-PL",
          "name": "SUMA.SZER.POT"
        },
        {
          "locale": "pt-BR",
          "name": "SERIESSUM"
        },
        {
          "locale": "pt-PT",
          "name": "SOMASÉRIE"
        },
        {
          "locale": "ro-RO",
          "name": "SERIESSUM"
        },
        {
          "locale": "ru-RU",
          "name": "РЯД.СУММ"
        },
        {
          "locale": "sk-SK",
          "name": "SERIESSUM"
        },
        {
          "locale": "sl-SI",
          "name": "SERIESSUM"
        },
        {
          "locale": "sr-Latn-RS",
          "name": "SERIESSUM"
        },
        {
          "locale": "sv-SE",
          "name": "SERIESUMMA"
        },
        {
          "locale": "th-TH",
          "name": "SERIESSUM"
        },
        {
          "locale": "tr-TR",
          "name": "SERİTOPLA işlevi"
        },
        {
          "locale": "uk-UA",
          "name": "SERIESSUM"
        },
        {
          "locale": "vi-VN",
          "name": "SERIESSUM"
        },
        {
          "locale": "zh-CN",
          "name": "SERIESSUM"
        },
        {
          "locale": "zh-HK",
          "name": "SERIESSUM"
        },
        {
          "locale": "zh-TW",
          "name": "SERIESSUM"
        }
      ],
      "signature": {
        "display": "SERIESSUM(x, n, m, coefficients)",
        "parameters": [
          {
            "description": null,
            "name": "x",
            "optional": false,
            "repeats": false
          },
          {
            "description": null,
            "name": "n",
            "optional": false,
            "repeats": false
          },
          {
            "description": null,
            "name": "m",
            "optional": false,
            "repeats": false
          },
          {
            "description": null,
            "name": "coefficients",
            "optional": false,
            "repeats": false
          }
        ],
        "trailing_repeats": false
      },
      "surface_name": "SERIESSUM",
      "version_marker": null,
      "xlcall": {
        "code": "414",
        "symbol": "xlfSeriessum"
      }
    },
    "microsoft": "https://support.microsoft.com/en-us/office/seriessum-function-a3ab25b5-1093-4f5b-b084-96c49087f637"
  },
  "try_it": {
    "formula": "=SERIESSUM(2,0,1,{1,3,2})"
  },
  "url": "https://handbook.dnacalc.com/functions/SERIESSUM.html",
  "variants": [],
  "versions": []
}