Pascal's triangle is a triangle that works in the following way.
The sum of the numbers in each row is 2 to the nth power. (Remember, the first row is row zero.)
Except for the first column, if one alternates the sum and difference (difference first), the value is always 0.
Row 2: 1 - 1 = 0
Row 3: 1 - 2 + 1 = 0
Row 4: 1 - 3 + 3 -1 = 0
The triangle can also be viewed as follows:
This can be used to prove the identity that
The -th row of the triangle, starting with zeroth row, represents the coefficients of the binomial expansion .