In this article
SERIESSUM adds a power series a1·x^n + a2·x^(n+m) + …, e.g. to approximate e^x or sin(x) with a few terms.
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Syntax
=SERIESSUM(x, n, m, coefficients)| Argument | What it means |
|---|---|
x |
Input value |
n |
First power |
m |
Step between powers |
coefficients |
a1, a2, … |
Examples
Example 1
=ROUND(SERIESSUM(A2,0,1,{1,1,0.5,0.1666667,0.0416667}),5)Result: 2.70833. See the worked example table below for more cases.
SERIESSUM in practice
Where you will use it
- Approximating e^x or sin x
- Polynomial models
- Numerical methods teaching
Worked example
| x | Formula | Result |
|---|---|---|
| 1 | =ROUND(SERIESSUM(A2,0,1,{1,1,0.5,0.1666667,0.0416667}),5) | 2.70833 |
| 0.5 | =ROUND(SERIESSUM(A3,0,1,{1,1,0.5,0.1666667,0.0416667}),5) | 1.64844 |
| 2 | =ROUND(SERIESSUM(A4,0,1,{1,1,0.5,0.1666667,0.0416667}),5) | 7 |
Results calculated in Excel. First 5 terms of the series for e^x: compare with EXP(x).
Mistakes people make
| Mistake | What to do instead |
|---|---|
| Too few terms | Approximation drifts for large x |
| Coefficients as text | Use numbers |
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