Documentation/How Tos/Calc: SERIESSUM function

SERIESSUM

Sums the first terms of a power series.

This function is only available if the Analysis AddIn is installed.

Syntax:

SERIESSUM(x; n; m; ar)

A power series may be represented as:

The SERIESSUM function calculates the sum of the first terms of such a series, where:

x is the variable,

n is the power of x for the first term,

m is the increment by which the power of x increases with each term, and

ar refers to a range containing the a coefficients of the terms to be included.

Example:

The following power series may be used to express the mathematical constant e raised to a power:

When x = 1, summing the terms in the series will approximate e. To sum the first 5 terms using SERIESSUM we should set:

x = 1

n = 0

m = 1

ar to B1:B5, where B1, B2, B3, B4, B5 contain respectively:

= 1/FACT(0), = 1/FACT(1), = 1/FACT(2), = 1/FACT(3), = 1/FACT(4)

Now, using these values in the SERIESSUM function:

SERIESSUM(1; 0; 1; B1:B5)

returns 2.70833333333333, an approximation of e ( = 2.71828182845904...). Using more terms would give a closer approximation.