Difference between revisions of "Manuals/calci/PASCALTRIANGLE"

Revision as of 23:52, 5 January 2014

PASCALTRIANGLE(r)

This function gives the Coefficients of the Pascal triangle.
In $PASCALTRIANGLE(r)$ , 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 :

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

                 1       1

                 1       1
                 1       2         1

PASCALTRIANGLE(level)

where

level is any real number

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

PASCALTRIANGLE returns NaN if level is not a real number.

PASCALTRIANGLE

Lets see an example in (Column2Row1)

?UNIQ9eec20026ff870ff-nowiki-00000002-QINU?

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

Syntax

Remarks

Examples

Description

$

@@ Line 9: / Line 9: @@
 *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 :
-<math>(x+y)^n=\sum_{k=0}^n \binom{n}{k}x^{n-k} .y^k </math>.    where <math> \binom{n}{k}</math> is the binomial coefficient.
+<math>(x+y)^n=\sum_{k=0}^n \binom{n}{k}x^{n-k} .y^k </math>.    where <math> \dbinom{n}{k}</math> is the binomial coefficient.
 *This function will return the result as error when the r <math> \le 0</math>.
 ==Examples==
-#PASCALTRIANGLE(1)=1
+*1.PASCALTRIANGLE(1)=1
-#PASCALTRIANGLE(2)=1
+*2.PASCALTRIANGLE(2)=1
        1
-#PASCALTRIANGLE(3)=1
+*3.PASCALTRIANGLE(3)=1
        1
        2         1
-#PASCALTRIANGLE(0)=NULL
+*4.PASCALTRIANGLE(0)=NULL