what are some mysteries pf pascals triangle?

Answer 1

Each row coresponds to coeficients of the binomial expansion. The first row is the n=0 row with the entry 1, the second row n=1 with the entries 1,1 and so on. The entries correspond to the coefficients of (a+b)^n.

Also you can get relationships between the entries of pascal's triangle and the fibonaci numbers. There are many other applications and patterns to be found.

Answer 2

I know this answer. In Row1 : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Relate with Row3: 1 3 6 10 15 21 28 36 45 55 66
and Row2 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Relate with Row4: 1 4 10 20 35 56 84 120 165 220 ................................................................................................................................................................ ..