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Math function
SERIESSUM
Returns the sum of a power series based on a formula.
Rarely usedDifficulty 1500 · AdvancedUsage rank #407 of 520
When to use it
Sums a power series: a1·x^n + a2·x^(n+m) + a3·x^(n+2m) … with the coefficients you supply. Taylor approximations and polynomial evaluation.
The shape of it
- Syntax
=SERIESSUM(x, n, m, coefficients)
Worked examples
Powers of two
=SERIESSUM(2,1,1,{1,1,1}) → 14
2 + 4 + 8.
Cosine by series
=SERIESSUM(PI()/4,0,2,{1,-1/2,1/24,-1/720}) → 0.707103
Four terms of the cosine series at 45°, close to 0.7071068.
Geometric terms
=SERIESSUM(0.5,1,1,{100,100,100}) → 87.5
50 + 25 + 12.5.
Worth knowing
- Evaluate a polynomial a0 + a1x + a2x²: SERIESSUM(x,0,1,{a0,a1,a2}).
- Coefficients can be a range instead of an array constant.
- For actual trig use SIN and COS; the series form is for teaching and custom expansions.
Where it goes wrong
- #VALUE! when any argument is not numeric.
- Blank coefficients count as zero terms.
Related
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