Difference between revisions of "Manuals/calci/PASCALTRIANGLE"
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| − | <div style="font-size:30px">'''PASCALTRIANGLE( | + | <div style="font-size:30px">'''PASCALTRIANGLE (Levels)'''</div><br/> |
| − | *<math> | + | *<math>Levels</math> 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== | ==Description== | ||
*This function gives the Coefficients of the Pascal triangle. | *This function gives the Coefficients of the Pascal triangle. | ||
| − | *In <math>PASCALTRIANGLE( | + | *In <math>PASCALTRIANGLE(Levels)</math> , <math>Levels</math> is the level number of the Pascal triangle. |
*Pascal triangle is the arrangement of numbers of the Binomial coefficients in a triangular shape. | *Pascal triangle is the arrangement of numbers of the Binomial coefficients in a triangular shape. | ||
*It is started with the number <math>1</math> at the top in the 1st row. | *It is started with the number <math>1</math> at the top in the 1st row. | ||
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==See Also== | ==See Also== | ||
*[[Manuals/calci/BINOMDIST | BINOMDIST ]] | *[[Manuals/calci/BINOMDIST | BINOMDIST ]] | ||
| + | *[[Manuals/calci/Pascal Triangle Fun | Pascal Triangle Fun Facts ]] | ||
==References== | ==References== | ||
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| − | [[Z_API_Functions | List of Main Z Functions]] | + | *[[Z_API_Functions | List of Main Z Functions]] |
| − | [[ Z3 | Z3 home ]] | + | *[[ Z3 | Z3 home ]] |
Latest revision as of 16:34, 6 August 2020
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
See Also
References