Manuals/calci/PASCALTRIANGLE

PASCALTRIANGLE (Levels)

• $Levels$ 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 $PASCALTRIANGLE(Levels)$ , $Levels$ 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 $1$ 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 :

$(x+y)^{n}=\sum _{k=0}^{n}{\binom {n}{k}}x^{n-k}.y^{k}$. where ${\dbinom {n}{k}}$ is the binomial coefficient.

• This function will return the result as error when $r\leq 0$.

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

• BINOMDIST

References

• Pascal's Triangle

• List of Main Z Functions

• Z3 home