# Pascal's triangle

The Pascal's triangle, named after Blaise Pascal, a famous french mathematician and philosopher, is shown below with 5 rows.

The calculator on this page can show Pascal's triangle for up to 99 rows.

Some Important things to notice

• The first row starts with 1
• Starting with row #2, the row starts and ends with 1.
• The number 2  in the third row is found by 1 and 1 in the second row
• The number 3 in the fourth row is found by adding 1 and 2 in the third row.
• The number 4 in the fifth row is found by adding 1 and 3 in the fourth row. The number 6 in the fifth row in found by adding 3 and 3 in the fourth row.

You can indeed keep building more rows by doing just that. It is not that complicated.

1

1                1

1                2                 1

1                 3                   3                 1

1                 4                  6                   4                 1

1

1                1

1                2                 1

1                 3                   3                 1

1                 4                  6                   4                 1

The Pascal's triangle can also be obtained by pulling out the coefficients of (a + b)n

We show the expansion of 4 binomials when n = 0, 1, 2, and 3.

You can really see the coefficients when n = 1. When n = 0, it is just the number 1 that we put on top on row #1.

(a + b)0 = 1

(a + b)1 = a + b = 1a + 1b

(a + b)2 = a2 + 2ab + b2 = 1a2 + 2ab + 1b2

a3 + 3a2b + 3ab2 + b3 = 1a3 + 3a2b + 3ab2 + 1b3

## Pascal's triangle calculator

This calculator will first show the expansion (a + b)n followed immediately by the triangle.

Enter a positive integer:

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