Manuals/calci/PASCALTRIANGLE

PASCALTRIANGLE(r)

• $r$ 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 \dbinom{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

• 3.PASCALTRIANGLE(3)=1

                 1       1
                 1       2         1

• 4.PASCALTRIANGLE(0)=NULL

References

• Pascal's Triangle