Each number in Pascal's Triangle is the sum of the number directly above it and the number to the immediate left of that number. The start of Pascal's Triangle is shown below, where the top row, containing just one 1, is row 0.
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 |
Pascal's Triangle is very important for binomial expansions.
The notations used for a number in Pascal's Triangle are:
- $\left(n\\r\right)$
- $_^nC_r$
where $n$ is the row number and $r$ is the $r^{th}$ term in the $n^{th}$ row
e.g. $\left(4\\3\right)=6$
The formula for finding any number in Pascal's Triangle is:
- $\left(n\\r\right)=\frac{n!}{r!(n-r)!}$
where $n!$ is n factorial
See http://mathworld.wolfram.com/PascalsTriangle.html for more information.
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