Difference between revisions of "Documentation/How Tos/Calc: SERIESSUM function"
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== SERIESSUM == | == SERIESSUM == | ||
Sums the first terms of a power series. | Sums the first terms of a power series. | ||
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This function is only available if the '''Analysis AddIn''' is installed. | This function is only available if the '''Analysis AddIn''' is installed. | ||
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=== Syntax: === | === Syntax: === | ||
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:: <tt>'''m'''</tt> is the increment by which the power of <tt>'''x'''</tt> increases with each term, and | :: <tt>'''m'''</tt> is the increment by which the power of <tt>'''x'''</tt> increases with each term, and | ||
:: <tt>'''ar'''</tt> refers to a range containing the <tt>'''a'''</tt> coefficients of the terms to be included. | :: <tt>'''ar'''</tt> refers to a range containing the <tt>'''a'''</tt> coefficients of the terms to be included. | ||
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=== Example: === | === Example: === | ||
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: returns <tt>'''2.70833333333333'''</tt>, an approximation of <i>e</i> ( = 2.71828182845904...). Using more terms would give a closer approximation. | : returns <tt>'''2.70833333333333'''</tt>, an approximation of <i>e</i> ( = 2.71828182845904...). Using more terms would give a closer approximation. | ||
| − | + | {{SeeAlso|EN| | |
| − | + | * [[Documentation/How_Tos/Calc: Mathematical functions|Mathematical functions]] | |
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| + | * [[Documentation/How_Tos/Calc: Functions listed alphabetically|Functions listed alphabetically]] | ||
| + | * [[Documentation/How_Tos/Calc: Functions listed by category|Functions listed by category]]}} | ||
| + | [[Category: Documentation/Reference/Calc/Mathematical functions]] | ||
Latest revision as of 15:41, 31 January 2024
Trigonometric
Hyperbolic
Rounding and remainders
Logarithm/Powers
Bessel functions
Miscellaneous
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.
See Also
