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.

Pascal's Triangle - dCode

Tag(s) : Arithmetics, Series

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The principle of **Pascal triangle** is based on a pyramidal/triangular construction, write 1 on the first line, and 1 1 on the second line. For the next lines, take two adjacent numbers, add their values and place this new number directly above. (The missing start and end are equal to 1).

__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

1 6 15 20 15 6 1

1 7 21 35 35 21 7 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.

Usually, mathematicians call the first line `0`, same for the first column.

A value $ V $ of the **Pascal triangle** at the position (line A, column B, 0-indexed) can be calculated with the binomial coefficients (and thus with factorials) and the formula $$ V = \binom{A}{B} = \frac{A!}{B!(A-B)!} $$

Write `1` in the cell `B1`, and `=A2+B1` in the cell `B2` and copy the contents in as many cells as you wish but do not touch column 1 and line 1. Each line is a new row of the **Pascal triangle**.

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