PlanMaker SERIESSUM: Power Series, Coefficients and Polynomial Checks

The PlanMaker 2026 reference, 2024 reference and 2021 reference document this function. Original introduction and last-working-version endpoints remain unverified; a manual family is not a test of every build or edition.

References were retrieved on October 15, 2026. No native PlanMaker execution was performed. Examples below are independently calculated expectations, not application screenshots or native results. FreeOffice/mobile edition coverage and file transfers are not certified. English formulas use commas; verify separators and names in your installation.

=SERIESSUM(x, n, m, Coefficients)

All four arguments are supplied. x is the base, n is the first exponent, and m is the exponent increment. For coefficients a1,a2,a3,…, the sum is a1×x^n+a2×x^(n+m)+a3×x^(n+2m)+… . The coefficient count determines the number of terms.

The 2024 and 2026 manuals describe Coefficients as a cell reference or a single-column array. The 2021 manual uses the broader wording of a one-dimensional cell range or array. This is a documentation difference, not proof of native row-array acceptance or rejection in any build. The examples here use columns throughout. The first coefficient belongs to the lowest indexed term, which need not have exponent zero. No optional argument or default is documented.

Create SeriesControls. Put x in A1 and 2 in B1, First_exponent in A2 and 2 in B2, Step in A3 and 1 in B3. Put Coefficient in D1, Exponent in E1 and Term in F1. Enter D2:D6 below. E2 is =$B$2, E3 is =E2+$B$3 filled through E6, and F2 is =D2*$B$1^E2 filled through F6.

In B5 enter =SERIESSUM(B1,B2,B3,D2:D6). The expected result is 516, equal to =SUM(F2:F6). This also reproduces the vendor’s =SERIESSUM(2,2,1,{1;2;3;4;5}) example. Semicolons separate rows within this column-array constant.

In a copy change B1 from 2 to 1. The terms become 1,2,3,4,5, and B5 becomes 15. Change only the base for this control; changing both the base and coefficients would make the source of the difference harder to audit.

For p(x)=3−2x+5x³, place 3,−2,0,5 in H2:H5. Use =SERIESSUM(2,0,1,H2:H5) to obtain 39. The zero coefficient preserves the missing x² term. Omitting it would incorrectly move 5 to the x² term, producing a different polynomial.

With x=3, the same coefficients give 132. At x=2, the direct control =3-2*2+5*2^3 also gives 39. Coefficient order is part of the formula, not a cosmetic arrangement that may be sorted freely.

Put 1,2,3 in J2:J4. =SERIESSUM(2,1,2,J2:J4) represents x+2x³+3x⁵ at x=2 and has expected value 114: 2+16+96. Increasing the first exponent to 2 multiplies every term by x, so =SERIESSUM(2,2,2,J2:J4) gives 228.

The increment m changes the gap between successive powers. It does not change the coefficient positions, and it is not the number of terms. Here there are three terms because there are three coefficient cells.

Put 1,1,0.5 in L2:L4. =SERIESSUM(0.1,0,1,L2:L4) returns the quadratic expression 1+x+x²/2, with exact expectation 1.105. EXP(0.1) is approximately 1.1051709181, so this finite polynomial is close but not equal to the exponential.

Changing x to 0.2 gives polynomial value 1.22, while EXP(0.2) is approximately 1.2214027582. The truncation error belongs to the chosen approximation; adding SERIESSUM does not sum terms whose coefficients were never supplied.

The short reference does not give a complete error/coercion table for blank or text coefficients, malformed ranges, arrays in the other arguments, or undefined powers. These examples use explicit numeric coefficients, positive bases and nonnegative integer exponents. Exact native behavior outside that scope remains unverified.

Check the first exponent, step and coefficient order before blaming numerical accuracy. Confirm that a copied formula retains the intended absolute parameter references. When array-constant separators differ by locale, a visible single-column cell range is the simplest way to keep the coefficients auditable.