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SERIESSUM Function (LibreOffice Calc)

Math Beginner LibreOffice Calc

Learn the SERIESSUM function in LibreOffice Calc: Returns the sum of a power series.

Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in LibreOffice Calc. How formula examples are checked

Historical validation scope: Native observations refer to saved LibreOffice Calc 25.2.3.2 Linux evidence dated 13 October 2026 at 00:06 UTC. This later review checked all artifact hashes and all 60 ODS/result pairs, and independently recalculated the series and sample-kurtosis examples. Calc was not rerun.

SERIESSUM adds a finite number of terms from a power series. It is useful when a calculation is naturally expressed as a polynomial, a geometric series, or an approximation built from increasing powers of an input. For an ordinary list of numbers, use SUM instead. [S1]

Validation scope (13 October 2026): Examples described as native-tested were executed in LibreOffice Calc 25.2.3.2 on Linux using a reproducible .ods workbook, and their numerical results were compared with separate Python calculations. The official online reference was the LibreOffice 26.8 Help page. The testing did not execute Calc 26.8, Microsoft Excel, or Google Sheets.

Official syntax, argument order, and mathematical meaning

=SERIESSUM(X; N; M; Coefficients)
Argument Type and role Required? Practical meaning
X Number or numeric cell expression Yes The value x at which to evaluate the series.
N Numeric starting exponent Yes Exponent used for the first coefficient.
M Numeric change in exponent Yes Amount added to the exponent for each next coefficient.
Coefficients Numeric coefficient sequence, usually a cell range Yes Ordered coefficients c₀, c₁, ...; each provides one additional term.

All four argument positions are required. There is no optional or implicit default for X, N, M, or Coefficients in the official syntax. The examples use the semicolon argument separator shown in LibreOffice’s English-language Help. In a locale with a different decimal separator or user-defined formula separator, use what your installed Calc formula editor shows; do not blindly paste a comma-delimited Excel example. [S1]

With coefficients c₀, c₁, …, cₖ, Calc evaluates the finite sum

c₀ × X^N + c₁ × X^(N+M) + c₂ × X^(N+2M) + … + cₖ × X^(N+kM).

The sequence order matters: the first coefficient multiplies the first power, the second coefficient multiplies the next power, and so forth. Coefficient values can be negative; the increment M can be zero or negative in the tested Calc 25.2 build. The function does not automatically determine an infinite-series limit or an approximation tolerance. [S1; N1]

Example 1: evaluate a polynomial with a coefficient range

To compute 1 + 2x + 3x² at x = 2, enter the following values in a new Calc sheet:

Cell Value Role
A2 2 Input x
B2 1 Coefficient for x⁰
B3 2 Coefficient for x¹
B4 3 Coefficient for x²

Enter in C2:

=SERIESSUM(A2;0;1;B2:B4)

Native observed result: 17. This is independently reproducible as 1 × 2⁰ + 2 × 2¹ + 3 × 2² = 1 + 4 + 12 = 17. Changing A2 to 1 gives 6; changing it to 3 gives 34. All three values match the examples in LibreOffice’s official mathematical-functions Help and were verified with the same coefficients in Calc 25.2.3.2. [S1; N1]

Tip: To reuse the same coefficients when copying the formula down, lock the range: =SERIESSUM(A2;0;1;$B$2:$B$4). The $ signs hold the coefficient range fixed while the input cell reference can change. Check that the new input cells do not overlap the coefficient cells.

Example 2: a finite geometric series

Suppose B2:B7 each contains the number 1. This formula sums the first six terms 1 + x + x² + x³ + x⁴ + x⁵:

=SERIESSUM(0.5;0;1;B2:B7)

Native observed result: 1.96875. Independent arithmetic: 1 + 0.5 + 0.25 + 0.125 + 0.0625 + 0.03125 = 1.96875. Six equal coefficients do not mean the exponents remain equal: M=1 increases the exponent by one per term. [N1]

For x = 2, the same six coefficients yield 63. For x = −0.5, they yield 0.65625. Those are finite sums, not predictions about convergence as the number of terms approaches infinity. [N1]

Example 3: approximate sine using a short Taylor series

The first four nonzero terms of the Taylor expansion for sin(x) around zero are:

x − x³/3! + x⁵/5! − x⁷/7!.

Enter the four coefficients in this exact order:

Cell Entry (Calc evaluates it as a number) Meaning
B2 1 x coefficient
B3 =-1/6 x³ coefficient
B4 =1/120 x⁵ coefficient
B5 =-1/5040 x⁷ coefficient

Enter:

=SERIESSUM(1;1;2;B2:B5)

Native observed result: approximately 0.841468253968254. The independently evaluated four-term polynomial agrees. The true value of SIN(1) is approximately 0.8414709848, so a finite truncated series introduces approximation error. The input is in radians for this trigonometric application, just as for Calc’s SIN function. Do not label this four-term approximation an exact sine value. [S1; N1; S4]

At x=0.5, the same series gives approximately 0.479425533234127; at x=−1 it gives approximately −0.841468253968254. Adding accurate higher-order terms improves the approximation over a suitable interval, but also increases the risk of numerical cancellation or overflow for unsuitable values. [N1]

Example 4: approximate cosine, and understand the starting exponent

The first four nonzero cosine terms around zero are 1 − x²/2! + x⁴/4! − x⁶/6!. Put 1, =-1/2, =1/24, =-1/720 in B2:B5, then use:

=SERIESSUM(1;0;2;B2:B5)

Native observed result: approximately 0.540277777777778 versus COS(1) ≈ 0.5403023059. Here N=0 starts at a constant term; M=2 selects even powers. The first 1 coefficient is essential. At x=0.5, the four-term polynomial gives approximately 0.877582465277778. [N1; S4]

Advanced examples: constant exponents, decreasing powers, and fractions

Make the exponent the same for every term. With B2:B4 equal to 1, 2, 3, this formula returns 24:

=SERIESSUM(2;2;0;B2:B4)

Because M=0, each coefficient multiplies 2², giving (1+2+3) × 4 = 24. This is useful for understanding the argument, though in a production model a simpler expression may be clearer. [N1]

Step powers down rather than up. With B2:B4 still containing 1, 2, 3:

=SERIESSUM(2;4;-2;B2:B4)

Native observed result: 27 from 1×2⁴ + 2×2² + 3×2⁰ = 16 + 8 + 3. A negative M was accepted by Calc 25.2.3.2 in this test, but readers using another version should verify the behavior. [N1]

Fractional powers were accepted for positive bases in the tested version. With coefficients 1, 2, 3, =SERIESSUM(4;0.5;0.5;B2:B4) yielded 34: 1×4^0.5 + 2×4^1 + 3×4^1.5 = 2 + 8 + 24. Fractional exponents with negative bases are not generally real-valued and may produce an argument error. [N1]

Errors and limitations — checked against the tested Calc version

Symptom What was observed in Calc 25.2.3.2 What to check
#VALUE! (error 519) =SERIESSUM("dog";0;1;B2:B4) X is text that is not usable as a number. Replace it with a numeric cell.
Err:504 =SERIESSUM(2;0;1) Required coefficients argument is missing.
Err:502 =SERIESSUM(-2;0.5;1;B2:B4) The fractional power of a negative base is outside the real-number domain in this case.
Err:502 =SERIESSUM(1E100;4;1;B2:B4) Magnitudes can exceed valid floating-point calculation limits. Scale the input or reduce powers.
#VALUE! (error 519) =SERIESSUM(0;0;1;B2:B4) The zero-base/zero-exponent case (0⁰) did not return the ordinary polynomial constant in this tested build; avoid assuming a portable result.
An unexpectedly small total A coefficient cell containing text n/a contributed as zero in the tested range Use numeric coefficients; review imported text and blanks.
A surprising coefficient order Range values are applied in worksheet order Put coefficients from the lowest starting exponent upward (or in the deliberate order required by a negative step).

A deliberately blank coefficient cell also contributed zero in an observed three-term series; neither that behavior nor the 0⁰ handling is asserted as a universal guarantee for all platforms/versions. An argument text value such as quoted "2" was coerced to 2 in one diagnostic case; prefer unquoted numeric inputs, not implicit coercion. Full diagnostic records are included in the saved dated evidence. [N1]

Important: This function sums entered coefficients; it does not automatically stop when terms are small, validate the approximation range, or provide an error bound. Recheck sign, factorial, and exponent patterns when translating an analytic series. [S1; N1]

SERIESSUM vs SUM, POWER, and SUMPRODUCT

SERIESSUM is a concise representation of coefficients multiplied by regularly stepped powers of one variable. SUM totals values you have already computed, POWER raises one value to one exponent, and SUMPRODUCT multiplies paired entries and adds the products. If each term needs a different or conditional calculation, an explicit helper column may be easier to audit. [S1]

LibreOffice, Excel, Google Sheets, and formula naming

Program What documentation supports What was actually run for this guide
LibreOffice Calc 25.2.3.2 Calc syntax SERIESSUM(X;N;M;Coefficients) and the finite power-series definition Recorded native execution: 19 independent-result tests, all passed; 12 diagnostics observed.
LibreOffice online 26.8 Help Same displayed Calc function syntax and official polynomial example Documentation checked; 26.8 not executed.
Microsoft Excel Microsoft documents SERIESSUM(x,n,m,coefficients) (commas in en-US examples) Documentation checked only; edge-case parity not established. [E1]
Google Sheets Google documents SERIESSUM(x,n,m,coefficients) Documentation checked only; edge-case parity not established. [G1]

This tutorial uses the function name displayed in English-language Calc. Formula separators and decimal marks depend on locale. A UNO API diagnostic stored the internal form COM.SUN.STAR.SHEET.ADDIN.ANALYSIS.GETSERIESSUM; that is not an extra user-facing worksheet function and should not be substituted into reader examples. Cross-format ODF internal names and precise historic introduction versions were not independently confirmed, so neither is claimed here. [N1]

How this guide was checked

The sample workbook contains a copyable polynomial example and sine/cosine coefficient tables. A separate script opened LibreOffice Calc 25.2.3.2 in headless mode through the LibreOffice UNO interface. For 19 numeric cases, recorded Calc outputs were compared against independent Python term-by-term sums (not derived from the cell outputs), and all 19 matched within declared numeric tolerance. Twelve additional invalid/edge inputs were observed without treating their error outputs as passed math assertions. Testing occurred 13 October 2026 (UTC), on Linux. The program version is different from the current 26.8 version selector displayed in the online Help, so future Calc behavior is not guaranteed. [N1]

Official documentation and claim references (accessed 13 October 2026)