Difference between revisions of "Documentation/How Tos/Calc: SERIESSUM function"

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{{DISPLAYTITLE:SERIESSUM function}}
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{{Documentation/CalcFunc MathematicalTOC
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|booktitle=<div style="padding: 8px; font-size: 140%; font-weight: bold; background-color: #9BC0F5;">CALC FUNCTIONS</div>
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|ShowParttitle=block|parttitle=[[Documentation/How_Tos/Calc:_Mathematical_functions|<div style="font-size: 140%;">Mathematical Functions]]
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|toccontent= <div style="padding: 4px; font-size: 130%; font-weight: hidden; background-color:#DCE9FC;">FUNCTIONS</div>
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<div style="font-size: 140%; border-style: outset outset outset none; border-color:#DCE9FC;">Trigonometric</div>
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* [[Documentation/How_Tos/Calc:_COS_function|<div style="font-size: 120%;">Cos]]
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* [[Documentation/How_Tos/Calc:_SIN_function|<div style="font-size: 120%;">Sin]]
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* [[Documentation/How_Tos/Calc:_TAN_function|<div style="font-size: 120%;">Tan]]
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* [[Documentation/How_Tos/Calc:_COT_function|<div style="font-size: 120%;">Cot]]
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* [[Documentation/How_Tos/Calc:_ACOS_function|<div style="font-size: 120%;">Acos]]
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* [[Documentation/How_Tos/Calc:_ACOT_function|<div style="font-size: 120%;">Acot]]
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* [[Documentation/How_Tos/Calc:_ASIN_function|<div style="font-size: 120%;">Asin]]
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* [[Documentation/How_Tos/Calc:_ATAN_function|<div style="font-size: 120%;">Atan]]
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* [[Documentation/How_Tos/Calc:_ATAN2_function|<div style="font-size: 120%;">Atan2]]
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* [[Documentation/How_Tos/Calc:_DEGREES_function|<div style="font-size: 120%;">Degrees]]
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* [[Documentation/How_Tos/Calc:_RADIANS_function|<div style="font-size: 120%;">Radians]]
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* [[Documentation/How_Tos/Calc:_PI_function|<div style="font-size: 120%;">Pi]]
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<div style="font-size: 140%; border-style: outset outset outset none; border-color:#DCE9FC;">Hyperbolic</div>
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* [[Documentation/How_Tos/Calc:_COSH_function|<div style="font-size: 120%;">Cosh]]
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* [[Documentation/How_Tos/Calc:_SINH_function|<div style="font-size: 120%;">Sinh]]
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* [[Documentation/How_Tos/Calc:_TANH_function|<div style="font-size: 120%;">Tanh]]
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* [[Documentation/How_Tos/Calc:_COTH_function|<div style="font-size: 120%;">Coth]]
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* [[Documentation/How_Tos/Calc:_ACOSH_function|<div style="font-size: 120%;">Acosh]]
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* [[Documentation/How_Tos/Calc:_ACOTH_function|<div style="font-size: 120%;">Acoth]]
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* [[Documentation/How_Tos/Calc:_ASINH_function|<div style="font-size: 120%;">Asinh]]
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* [[Documentation/How_Tos/Calc:_ATANH_function|<div style="font-size: 120%;">Atanh]]
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<div style="font-size: 140%; border-style: outset outset outset none; border-color:#DCE9FC;">Rounding and remainders</div>
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* [[Documentation/How_Tos/Calc:_TRUNC_function|<div style="font-size: 120%;">Trunc]]
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* [[Documentation/How_Tos/Calc:_ROUND_function|<div style="font-size: 120%;">Round]]
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* [[Documentation/How_Tos/Calc:_ROUNDDOWN_function|<div style="font-size: 120%;">Rounddown]]
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* [[Documentation/How_Tos/Calc:_ROUNDUP_function|<div style="font-size: 120%;">Roundup]]
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* [[Documentation/How_Tos/Calc:_CEILING_function|<div style="font-size: 120%;">Ceiling]]
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* [[Documentation/How_Tos/Calc:_FLOOR_function|<div style="font-size: 120%;">Floor]]
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* [[Documentation/How_Tos/Calc:_EVEN_function|<div style="font-size: 120%;">Even]]
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* [[Documentation/How_Tos/Calc:_ODD_function|<div style="font-size: 120%;">Odd]]
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* [[Documentation/How_Tos/Calc:_MROUND_function|<div style="font-size: 120%;">Mround]]
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* [[Documentation/How_Tos/Calc:_INT_function|<div style="font-size: 120%;">Int]]
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* [[Documentation/How_Tos/Calc:_QUOTIENT_function|<div style="font-size: 120%;">Quotient]]
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* [[Documentation/How_Tos/Calc:_MOD_function|<div style="font-size: 120%;">Mod]]
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<div style="font-size: 140%; border-style: outset outset outset none; border-color:#DCE9FC;">Logarithm/Powers</div>
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* [[Documentation/How_Tos/Calc:_EXP_function|<div style="font-size: 120%;">Exp]]
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* [[Documentation/How_Tos/Calc:_POWER_function|<div style="font-size: 120%;">Power]]
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* [[Documentation/How_Tos/Calc:_LOG_function|<div style="font-size: 120%;">Log]]
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* [[Documentation/How_Tos/Calc:_LN_function|<div style="font-size: 120%;">Ln]]
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* [[Documentation/How_Tos/Calc:_LOG10_function|<div style="font-size: 120%;">Log10]]
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<div style="font-size: 140%; border-style: outset outset outset none; border-color:#DCE9FC;">Bessel functions</div>
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* [[Documentation/How_Tos/Calc:_BESSELI_function|<div style="font-size: 120%;">Besseli]]
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* [[Documentation/How_Tos/Calc:_BESSELJ_function|<div style="font-size: 120%;">Besselj]]
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* [[Documentation/How_Tos/Calc:_BESSELK_function|<div style="font-size: 120%;">Besselk]]
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* [[Documentation/How_Tos/Calc:_BESSELY_function|<div style="font-size: 120%;">Bessely]]
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<div style="font-size: 140%; border-style: outset outset outset none; border-color:#DCE9FC;">Miscellaneous</div>
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* [[Documentation/How_Tos/Calc:_ABS_function|<div style="font-size: 120%;">Abs]]
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* [[Documentation/How_Tos/Calc:_COMBIN_function|<div style="font-size: 120%;">Combin]]
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* [[Documentation/How_Tos/Calc:_COMBINA_function|<div style="font-size: 120%;">Combina]]
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* [[Documentation/How_Tos/Calc:_CONVERT_function|<div style="font-size: 120%;">Convert]]
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* [[Documentation/How_Tos/Calc:_CONVERT_ADD_function|<div style="font-size: 120%;">Convert Add]]
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* [[Documentation/How_Tos/Calc:_COUNTBLANK_function|<div style="font-size: 120%;">Countblank]]
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* [[Documentation/How_Tos/Calc:_COUNTIF_function|<div style="font-size: 120%;">Countif]]
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* [[Documentation/How_Tos/Calc:_DELTA_function|<div style="font-size: 120%;">Delta]]
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* [[Documentation/How_Tos/Calc:_ERF_function|<div style="font-size: 120%;">Erf]]
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* [[Documentation/How_Tos/Calc:_ERFC_function|<div style="font-size: 120%;">Erfc]]
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* [[Documentation/How_Tos/Calc:_FACT_function|<div style="font-size: 120%;">Fact]]
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* [[Documentation/How_Tos/Calc:_FACTDOUBLE_function|<div style="font-size: 120%;">Factdouble]]
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* [[Documentation/How_Tos/Calc:_GCD_function|<div style="font-size: 120%;">Gcd]]
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* [[Documentation/How_Tos/Calc:_GCD_ADD_function|<div style="font-size: 120%;">Gcd Add]]
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* [[Documentation/How_Tos/Calc:_GESTEP_function|<div style="font-size: 120%;">Gestep]]
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* [[Documentation/How_Tos/Calc:_LCM_function|<div style="font-size: 120%;">Lcm]]
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* [[Documentation/How_Tos/Calc:_LCM_ADD_function|<div style="font-size: 120%;">Lcm Add]]
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* [[Documentation/How_Tos/Calc:_MULTINOMIAL_function|<div style="font-size: 120%;">Multinomial]]
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* [[Documentation/How_Tos/Calc:_PRODUCT_function|<div style="font-size: 120%;">Product]]
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* [[Documentation/How_Tos/Calc:_RAND_function|<div style="font-size: 120%;">Rand]]
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* [[Documentation/How_Tos/Calc:_RANDBETWEEN_function|<div style="font-size: 120%;">Randbetween]]
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* [[Documentation/How_Tos/Calc:_SERIESSUM_function|<div style="font-size: 120%; border-style: double; border-color:#778899;">Seriessum]]
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* [[Documentation/How_Tos/Calc:_SIGN_function|<div style="font-size: 120%;">Sign]]
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* [[Documentation/How_Tos/Calc:_SQRT_function|<div style="font-size: 120%;">Sqrt]]
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* [[Documentation/How_Tos/Calc:_SQRTPI_function|<div style="font-size: 120%;">Sqrtpi]]
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* [[Documentation/How_Tos/Calc:_SUBTOTAL_function|<div style="font-size: 120%;">Subtotal]]
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* [[Documentation/How_Tos/Calc:_SUM_function|<div style="font-size: 120%;">Sum]]
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* [[Documentation/How_Tos/Calc:_SUMIF_function|<div style="font-size: 120%;">Sumif]]
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* [[Documentation/How_Tos/Calc:_SUMSQ_function|<div style="font-size: 120%;">Sumsq]]
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}}__TOC__
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== SERIESSUM ==
 
== SERIESSUM ==

Latest revision as of 15:41, 31 January 2024

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:
power series
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:

power series

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
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