Pascal's Triangle

$1$ $1 \hspace{1cm} 1$ $1 \hspace{1cm} \boxed{2} \hspace{1cm} 1$ $1\hspace{1cm} 3 \hspace{1cm} \boxed{3} \hspace{1cm} 1$ $1\hspace{1cm} \boxed{4} \hspace{1cm} 6 \hspace{1cm} \boxed{4} \hspace{1cm} 1$

3rd line=> 1+1= 2, or 2+1=3, or 3+1=4 ,

------------------a1---------------------------------------------------------------------------------------------------------------------------------------------- ------------a2 --------a3--------------------------------------------------------------------------------------------------------------------------------------- --------a4 ------x -------- a5---------------------------------------------------------------------------------------------------------------------------------- ----a6------k -------y -------a7 ---------------------------------------------------------------------------------------------------------------------------
--a8 ---- z ------ j ------w ----- a9

a1= a2 = a3 = a4 = a5 = a6 = a7 = a8 = a9 = 1

x = a2 + a3 ; k = a4 + x ; y = x + a5 ; z = a6 + k ; j = k + y ; w = y + a7

the letters inside are found by total of the other 2 letters on its diagonal left and right above (see the formula pattern). for the side areas (a1,a2,...) are always be 1, by using this method, you can easily count for the next number

by using binomial hem, nth povver of (a+b) term , let n=1,2,3,4,5

the number missing is the sum of the two numbers above it

add top two numbers & write down below