Pascal's Triangle

Pascal's Triangle is used to find the coefficients of the expansion of (a+b)ⁿ, where n is positive.

For example :

(a+b)0	=	1
(a+b)0	=	1
(a+b)1	=	1a + 1b
(a+b)2	=	(a + b)(a + b )
	=	1a2 + 2ab + 1b2
(a+b)3	=	(a + b)(a + b)2
	=	(a + b)(a2 + 2ab + b2)
	=	a3 + a2b + 2a2b + 2ab2 + ab2 + b3
	=	1a3 + 3a2b + 3ab2 + 1b3
(a+b)4	=	(a + b)(a + b)3
	=	(a + b)(a3 + 3a2b + 3ab2 + b3)
	=	a4 + a3b + 3a3b + 3a2b2 + 3a2b2 + 3ab3 + ab3 + b4
	=	1a4 + 4a3b + 6a2b2 + 4ab3 + 1b4

Writing the coefficients of each expansion in a triangular form :

	1
	1    1
	1   2   1
	1   3   3   1
	1   4   6   4   1

It can be noticed that there is a pattern to form the coefficients :

	1
	1 + 1
	1   2   1
	1 + 3 +  3   1
	1   4   6   4   1

For example the expansion of (a+b)⁵ is :

1a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + 1b⁵

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