Consider the binomial [tex]\displaystyle{ (a+b)^\displaystyle{n[/tex],
where n=0, 1, 2, 3, ...
For example
[tex]\displaystyle{ (a+b)^0=1[/tex]
[tex]\displaystyle{(a+b)^1=1a+1b[/tex]
[tex]\displaystyle{(a+b)^2=1a^2+2ab+1b^2[/tex]
[tex]\displaystyle{ (a + b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3[/tex]
...
...
Consider the Pascal's triangle, as shown in the picture, where the very first row is denoted by row 0, the second by row 1, the third by row 2 and so on...
We notice that the coefficients of the expansion of [tex](a+b)^n[/tex], are the entries in the [tex]n^{th}[/tex] row of Pascal's triangle.
