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Pascal`s Identity and Triangle

Pascal’s Identity is a mathematical relationship that is closely associated with Pascal’s Triangle.

• It states that the sum of two adjacent entries in Pascal’s Triangle is equal to the entry immediately below them. Mathematically, it can be expressed as:

pas

Pascal’s Triangle is a triangular array of numbers where the outer edges are filled with ones, and each interior number is the sum of the two numbers directly above it.

pascalEquations
pascal triangle14

Q). Write down the expansion of (1+y)6, using Pascal`s theorem.

solution:

Here n=6, so we use Pascal`s triangle up to 6.
When n=0
When n=1
When n=2
When n=3
When n=4
When n=5
When n=6
pascal triangle
∴ (1+y)6 = 1(1)6 + 6(1)5y + 15(1)4y2 + 20(1)3y3+ 15(1)2y4 + 6(1)y5 + 1(1)0y6
= 1+6y+15y2+20y3+15y4+6y5+y6

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