SERIESSUM
Returns the sum of a power series: a·xⁿ + a·xⁿ⁺ᵐ + a·xⁿ⁺²ᵐ + ... Used to approximate functions like exp, sin, cos.
SERIESSUM(x, n, m, coefficients)Arguments
xThe input value of the power series.nThe initial power to which to raise x.mThe step by which to increase n for each term in the series.coefficientsA set of coefficients by which each successive power of x is multiplied.
=SERIESSUM(2,0,1,{1,1,1,1})1·1 + 1·2 + 1·4 + 1·8 = 15
=SERIESSUM(1,0,2,{1,-0.5,0.0833})Approximation of cos(1) via Taylor series
- •Returns #VALUE! if x, n, or m is non-numeric
- •Number of terms equals the count of coefficients
- •Useful for implementing Taylor and Maclaurin expansions
- •Mismatching the number of coefficients with the intended number of terms - SERIESSUM always uses exactly as many terms as there are coefficients, so an incomplete or truncated coefficients array silently produces a partial series sum
- •Confusing the roles of n and m - n sets the starting power of x, while m is the step size between successive powers, and swapping their intended values produces a completely different series
- •Passing text or non-numeric values anywhere in x, n, m, or coefficients, which returns a #VALUE! error rather than skipping the invalid term
SUMPRODUCTCan manually replicate a power series calculation with more flexibility, though SERIESSUM is more direct for the standard power-series pattern.POWERRaises a single value to a single power, the basic operation that SERIESSUM repeats and sums across multiple terms.TRENDFits data to a different kind of mathematical model (linear or polynomial trend), an alternative approach when a power series approximation isn't the right fit.How many terms does SERIESSUM add up?
Exactly as many as there are values in the coefficients array - each coefficient corresponds to one term in the series, with powers increasing by m each time starting from n.
What's the difference between the n and m arguments?
n is the starting exponent applied to x in the first term, while m is how much the exponent increases for each subsequent term - together they control which powers of x appear in the series.
Can SERIESSUM approximate functions like sine or cosine?
Yes, that's one of its most common uses - supplying the appropriate Taylor or Maclaurin series coefficients lets SERIESSUM approximate trigonometric, exponential, and other functions.
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