Pascal’s Triangle is a triangular array of binomial coefficients, where each number is the sum of the two directly above it.
Properties
- Symmetry: The triangle is symmetrical.
- Binomial Coefficients: Each row corresponds to the coefficients of .
- 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.