Pascal's Rule/Examples

Examples of Use of Pascal's Rule

$\binom 1 4$ plus $\binom 2 4$

\(\ds \dbinom 4 1 + \dbinom 4 2\) \(=\) \(\ds 4 + 6\)
\(\ds \) \(=\) \(\ds 10\)
\(\ds \) \(=\) \(\ds \dbinom 5 2\)


$\binom 1 5$ plus $\binom 2 5$

\(\ds \dbinom 5 1 + \dbinom 5 2\) \(=\) \(\ds 5 + 10\)
\(\ds \) \(=\) \(\ds 15\)
\(\ds \) \(=\) \(\ds \dbinom 6 2\)


$\binom 2 5$ plus $\binom 3 5$

\(\ds \dbinom 5 2 + \dbinom 5 3\) \(=\) \(\ds 10 + 10\)
\(\ds \) \(=\) \(\ds 20\)
\(\ds \) \(=\) \(\ds \dbinom 6 3\)
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.