English Español Deutsch 日本語 Français Português Русский Italiano Nederlands Polski

Quick Navigation

SERIESSUM Function

Excel 2007+

Summary

The Excel SERIESSUM function calculates the sum of a power series expansion using the formula: sum of coefficients[i] * x^(n + i*m). This powerful mathematical function enables approximation of complex functions through Taylor or Maclaurin series expansions directly within Excel spreadsheets.

Syntax

SERIESSUM(x, n, m, coefficients)

Parameters

Parameter Type Required Description
x Number Yes The base value x raised to successive powers in the series
n Number Yes Starting exponent for the first term (n, n+m, n+2m, etc.)
m Number Yes Increment by which exponents increase for each term
coefficients Array/Range Yes Coefficients multiplied by each corresponding power term

Using the SERIESSUM Function

SERIESSUM is essential for advanced mathematical calculations in Excel, particularly when approximating transcendental functions using their power series expansions. It handles the complex exponentiation and multiplication automatically based on the provided parameters.

Common SERIESSUM Examples

Cosine Approximation (π/4 radians)

=SERIESSUM(PI()/4,0,2,{0.785398163;-0.5;0.041666667;-0.001388889})

Approximates cos(π/4) ≈ 0.707 using first four terms of cosine series (result: 0.707103)

Using Formula Coefficients

=SERIESSUM(A3,0,2,A4:A7)

Uses cell range with formula-generated coefficients matching the table data for cosine approximation

Exponential Series

=SERIESSUM(0.5,0,1,{1;0.5;0.125;0.020833})

Approximates e^0.5 using first four terms of exponential series

Frequently Asked Questions

The number of values in the coefficients array determines how many terms are calculated.

Yes, negative coefficients are fully supported and common in alternating series like sine and cosine.

SERIESSUM handles non-integer exponents correctly using Excel's power function.

Common Errors and Solutions

#VALUE!

Cause: Any non-numeric argument provided

Solution: Ensure all inputs (x, n, m, coefficients) contain only numeric values

#VALUE!

Cause: Coefficients array is empty

Solution: Provide at least one coefficient value

Notes

  • Series formula: coefficients[0]*x^n + coefficients[1]*x^(n+m) + coefficients[2]*x^(n+2m) + ...
  • Perfect for Taylor series where n=0, m=1 (Maclaurin series)
  • Use for trigonometric (sin/cos), exponential, logarithmic approximations
  • Array coefficients can reference ranges or be entered directly as array constants

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+