The `SERIESSUM` function in Excel is used to calculate the sum of a power series. This function can be particularly useful when dealing with polynomial expansions or when approximating complex functions using a series. The general syntax for the `SERIESSUM` function is:
SERIESSUM(x, n, m, coefficients)
Here’s what each argument means:
- `x`: This is the input value to the series. It’s the variable that will be raised to successive powers defined by the series.
- `n`: The initial power to which `x` is raised.
- `m`: The increment by which the power of `x` is increased for each term in the series.
- `coefficients`: An array or range of coefficient values that are multiplied by each term of the series. Each coefficient corresponds to a term in the series, defining the series’ constants.
How it works:
The function calculates the sum of the series as follows:
[ text{SERIESSUM} = text{{coefficients}}_1 times x^n + text{{coefficients}}_2 times x^{n+m} + text{{coefficients}}_3 times x^{n+2m} + ldots ]
Example Usage:
Suppose you want to calculate the sum of the series defined by:
[ f(x) = 1 + 2x + 3x^2 + 4x^3 ]
Here, `x` is the variable, the initial power `n` is 0, the power increment `m` is 1, and the coefficients are {1, 2, 3, 4}.
You would set up the SERIESSUM function like this:
- Let’s assume `x` is 2.
- The initial power `n` is 0.
- Each subsequent term power is incremented by `m`, which is 1.
- The coefficients are {1, 2, 3, 4}.
The formula would be:
=SERIESSUM(2, 0, 1, {1, 2, 3, 4})
This would evaluate to:
[ 1 times 2^0 + 2 times 2^1 + 3 times 2^2 + 4 times 2^3 = 1 + 4 + 12 + 32 = 49 ]
Tips:
- Make sure the `coefficients` parameter is entered as an array or a continuous range in your worksheet.
- The `coefficients` array and any other ranges involved must have the same number of elements; otherwise, Excel will return an error.
- This function is especially useful for mathematical calculations involving series expansions like Taylor series or polynomial evaluations.
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