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Pascal's Triangle

Tool to compute value for Pascal's triangle. Pascal's Triangle is an arithmetic list of number imagined by Blaise Pascal where each item is either 1 or the sum of the two elements above it.

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Pascal's Triangle -

Tag(s) : Arithmetics, Series

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Pascal's Triangle

Pascal Triangle Calculator

Tool to compute value for Pascal's triangle. Pascal's Triangle is an arithmetic list of number imagined by Blaise Pascal where each item is either 1 or the sum of the two elements above it.

How to create a pascal triangle?

The principle is easy, write 1 on the first line, and 1 1 on the second line.

For the next lines, add the values of the two numbers directly above.

Example: Start of the Pascal Triangle :
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

Values can be calculated using binomial coefficient, also used in calculation of combinations.

Pascal triangle values can be compared to the Fibonacci sequence where each number is the sum of the two preceding numbers.

How to calculate a precise value in the Pascal's triangle?

A value $$V$$ of the Pascal triangle at the position (line A, column B) can be calculated with the binomial coefficients (and thus with factorials) and the formula $$V = \ binom {A} {B} = \ frac {A!} {B! (A-B)!}$$