1 1 . 1 1 . 2 . 1 1 . 3 . 3 . 1 1 . 4 . 6 . 4 . 1 1 . 5 . 10 . 10 . 5 . 1 1 . 6 . 15 . 20 . 15 . 6 . 1 etc Pascal's Triangle
Each number in Pascal's Triangle is the sum of the two numbers directly above. The start of Pascal's Triangle is shown here, where the top row, containing just one 1, is row 0.

Pascal's Triangle is very important for binomial expansions, the contents being the binomial coefficients.

The notations used for a number in Pascal's Triangle are:

• $n\choose~r$
• ${}^nC_r$
where $n$ is the row number and $r$ is the $r^{th}$ term in the $n^{th}$ row e.g. ${4\choose~2}~=~6$

The formula for finding any number in Pascal's Triangle is:

• ${n\choose~r}~=~\frac{n!}{r!(n-r)!}$
where $n!$ is $n$ factorial

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