Manuals/calci/PASCALTRIANGLE

PASCALTRIANGLE(r)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is the row number.

Description

• This function gives the Coefficients of the Pascal triangle.
• In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle PASCALTRIANGLE(r)} , r is the row number of the Pascal triangle.
• Pascal triangle is the arrangement of numbers of the Binomial coefficients in a triangular shape.
• It is started with the number 1 at the top in the 1st row.
• Then from the 2nd row each number in the triangle is the sum of the two directly above it.
• The construction is related to the binomial coefficients by Pascal's rule is :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x+y)^n=\sum_{k=0}^n \binom{n}{k}x^{n-k} .y^k } . where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \binom{n}{k}} is the binomial coefficient.

• This function will return the result as error when the r Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \le 0} .

Examples

1. PASCALTRIANGLE(1)=1
2. PASCALTRIANGLE(2)=1

                 1       1

1. PASCALTRIANGLE(3)=1

                 1       1
                 1       2         1

1. PASCALTRIANGLE(0)=NULL

References

• Pascal's Triangle

PASCALTRIANGLE(level)

where

level is any real number

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PASCALTRIANGLE function returns pascal's triangle for the given level.

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PASCALTRIANGLE returns NaN if level is not a real number.

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PASCALTRIANGLE

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Lets see an example in (Column2Row1)

?UNIQ9eec20026ff870ff-nowiki-00000002-QINU?

Returns 1,1,1,1,2,1 for PASCALTRIANGLE(3)

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Syntax

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Remarks

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Examples

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Description

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Default Calci

	Column1	Column2	Column3	Column4
Row1	3	1,1,1,1,2,1
Row2		File:Copy-cube.gif
Row3
Row4
Row5
Row6

File:Calci1.gif

$

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