Question

How Do You Do Pascal’s Triangle?

Answer 1

Pascal's triangle :
A triangular arrangement of number which give the coefficient in the expansion of ${\left(x+y\right)}^n$

For eg:

$$\begin{gathered} n=1 \\ {(x+y)}^1=x+y \\ n=2, \\ {(x+y)}^2=x^2+2xy+y^2 \\ n=3, \\ {(x+y)}^3=x^3+3x^{2}y+3x{y}^2+y^3 \end{gathered}$$

Pascal's triangle are as follows :

$$\begin{gathered} n=11 \\ n=2121 \\ n=31331 \\ n=414641 \\ n=515101051 \\ andsoon \end{gathered}$$

Hence, from the pascal triangle we can find the coefficient in expansion.