PASCAL’S  TRIANGLE

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

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