Manuals/calci/PASCALTRIANGLE

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PASCALTRIANGLE (Levels)


  • 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 Levels} is the level number of the Pascal Triangle.
    • PASCALTRIANGLE(), is a triangle of numbers in which a row represents the coefficients of the binomial series.

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(Levels)} , 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 Levels} is the level 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 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 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 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 \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

Related Videos

PASCAL'S TRIANGLE

See Also

References