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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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.

The principle of **Pascal triangle** is based on a triangular contruction, 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

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 note 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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