Zoho Sheet SERIESSUM: Power-Series and Polynomial Examples

Zoho’s official SERIESSUM reference was retrieved on October 15, 2026. This establishes documentation in the rolling web service, not the original introduction release or a final functioning-version endpoint; both historical endpoints remain unverified. Mobile/offline parity is not established. Additional numerical examples below were independently calculated. No native Zoho Sheet execution or cross-product import test was performed.

SERIESSUM(x; n; m; a)

All four arguments are required: x is the evaluation input, n the first exponent, m the exponent step, and a an array or range of coefficients. The first coefficient multiplies x^n, the second x^(n+m), and coefficient i multiplies x^(n+(i-1)*m). The array’s length determines the number of terms; m does not count them.

The official description abbreviates its mathematical expression as SERIES, while the explicit syntax names SERIESSUM. Use SERIESSUM in the worksheet. The documented examples reference hidden cell data, so the complete datasets here are supplied independently rather than inventing the vendor’s missing inputs.

Zoho’s English examples use semicolons between arguments. These examples use a vertical numeric coefficient range to make ordering explicit and avoid assuming undocumented two-dimensional traversal rules.

Create Polynomial, reserving A1:H8. Put Coefficient in F1 and numeric 3, -2, 5 in F2:F4. Put First_power in G1, Step in H1, numeric 0 in G2 and 1 in H2. In A1:D1 put x, Series, Expanded and Difference. Enter x values below and fill these formulas through row 7:

B2: =SERIESSUM(A2;$G$2;$H$2;$F$2:$F$4)
C2: =$F$2+$F$3*A2+$F$4*A2^2
D2: =B2-C2

D is mathematically zero. For the half-unit input, the fraction 13/4 means 3.25; set a decimal format if desired. Absolute references keep both the coefficients and exponent controls fixed during fill-down.

Duplicate Polynomial as ChangedCoefficient, then change F3 from -2 to -1. Each result increases by x: at x = 2 it becomes 21, while at x = -2 it becomes 25. This is a useful signed-input control; a coefficient increase does not necessarily increase every output.

In another copy of the original sheet, set G2 to 1 and keep H2 = 1. B now evaluates 3x - 2x² + 5x³. At x = 2 it is 38. Update C to the new expanded formula before expecting D = 0; leaving C as the quadratic intentionally creates a mismatch.

For G2 = 0 and H2 = 2, the series becomes 3 - 2x² + 5x⁴. At x = 2 the result is 75, and at x = -2 it is also 75. A power increment of two creates even exponents in this setup. It does not skip every other coefficient.

Create CosineApproximation. Enter coefficients as formulas in F2:F5: =1, =-1/2, =1/24, =-1/720. Put x values 0.5, 1, 2 in A2:A4. Fill B2 =SERIESSUM(A2;0;2;$F$2:$F$5), C2 =COS(A2) and D2 =B2-C2 through row 4.

The polynomial contains four supplied terms; SERIESSUM does not automatically add terms until a target accuracy is reached. The error grows over this selected range. That makes the table useful for understanding truncation, not for replacing COS in a general workbook. Zoho’s COS reference defines its argument in radians.

• Preserve coefficient order. Sorting coefficients destroys the intended polynomial.
• Preserve numeric zero coefficients if a power is absent. Deleting one shifts all later exponents unless you also redesign the series.
• Verify the $ signs after copying: a moving coefficient range evaluates a different series.
• Negative bases with fractional exponents, zero with zero or negative powers, text/blanks in coefficients, two-dimensional ranges and overflow are outside these worked cases. Their exact Zoho behavior is unverified.
• A small difference against an expanded formula may be floating-point rounding; a large difference usually calls for checking n, m, the range and coefficient order first.

The official shared glossary mentions invalid-type/name/reference errors, but does not provide a full function-specific edge-case table. Keep a manual expansion for a few known inputs before applying a large coefficient set. SUM adds existing terms; POWER evaluates individual powers. Neither alone supplies SERIESSUM’s ordered exponent progression. Matching names in another product do not guarantee identical blank handling or precision.