**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:

**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.

**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 |

∴ (1+y)^{6} = 1(1)^{6} + 6(1)^{5}y + 15(1)^{4}y^{2} + 20(1)^{3}y^{3}+ 15(1)^{2}y^{4} + 6(1)y^{5} + 1(1)^{0}y^{6} = 1+6y+15y ^{2}+20y^{3}+15y^{4}+6y^{5}+y^{6} |