Pascal’s Triangle is a triangular array of binomial coefficients, where each number is the sum of the two directly above it.

Properties

  1. Symmetry: The triangle is symmetrical.
  2. Binomial Coefficients: Each row corresponds to the coefficients of .
  3. Edges: The edges are always 1.

Pascal’s Triangle

           1
         1   1
       1   2   1
     1   3   3   1
   1   4   6   4   1
 1   5  10  10   5   1

Example: Expand

From the 4th row:

Expansion:

Formula for Binomial Expansion

For :

where .

Fun Facts

  • The sum of the entries in the row is .
  • The diagonal elements represent Fibonacci numbers.