SERIESSUM Function (Gnumeric)

• Introduced: Gnumeric 0.27 release notes explicitly record this function being added.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with the Mathematics plugin. English comma-separated formulas are shown.
• Checked: October 14, 2026. Tables and the named advanced check were recalculated through 1.12.57 ssconvert. Current 1.12.62 source was inspected; the later release was not executed.

SERIESSUM evaluates a finite series a₀xⁿ + a₁x⁽ⁿ⁺ᵐ⁾ + a₂x⁽ⁿ⁺²ᵐ⁾ + … from a coefficient range. It does not infer a convergent infinite series or estimate the error of a truncated approximation. Versioned function help.

=SERIESSUM(x,n,m,coefficients)

Function implementation.

Enter F2:F4 as 1, 2, 3, leave F5 empty and enter 4 in F6. For diagnostics, enter G2:G4 as 1, text abc, 2, and H2:H4 as Boolean TRUE, 2, 3.

Ordinary results are rounded to twelve decimal places; tiny values use scientific notation. The eight reference rows were independently checked.

With F2:F4 containing 1, 2, 3, =SERIESSUM(2,0,1,F2:F4) computes 1 + 2×2 + 3×2² = 17. The executed subtraction from this explicitly expanded expression returned zero. Increasing the initial exponent to 1 multiplies this example by x and gives 34. Increasing the step to 2 instead gives 1 + 2×2² + 3×2⁴ = 57.

Coefficient position determines exponent. To represent a missing term, put an explicit numeric zero in its coefficient cell. Do not leave that cell blank: blanks are omitted before the powers are assigned.

The table’s =SERIESSUM(4,0.5,0.5,F2:F4) is 1×4^0.5 + 2×4^1 + 3×4^1.5 = 34. This demonstrates numeric exponents beyond the narrower help description. With n = −1, x = 2 and step 1, the result is 0.5 + 2 + 6 = 8.5.

In F2:F6, the empty F5 is skipped, so the four coefficients 1, 2, 3, 4 receive consecutive powers. The tested result is 49, not the 81 obtained by reserving the blank position for a zero coefficient. Keep the coefficient count and order explicit when importing sparse data.

At x = 0 the implementation rejects a nonpositive first or last exponent. Thus =SERIESSUM(0,0,1,F2:F4) gives #NUM! even though a conventional polynomial would have constant term 1. For a positive initial exponent in the tested case, the result is zero. A negative base with a fractional exponent also produced #NUM!. Text and Boolean coefficients produced #VALUE!, rather than being silently omitted.

F5 is an actually empty cell. Listed errors are native error results, not mathematical zeroes.

• Worksheet implementation

The retained workbook contained a deliberately stale SUM cache and an uncached SUM formula, both recalculated correctly. Native evidence covers the listed 1.12.57 cases; worksheet layouts and algebraic interpretations are independently specified explanations. Other locales, direct GUI entry and later-release output were not tested.

SUM, ISNUMBER.