Pascal’s Triangle

A triangle full of patterns

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Pascal's triangle: each entry is the sum of the two above, and the entries are $\binom{n}{k}$.
• Row $n$ sums to $2^n$. The binomial theorem uses the rows as coefficients.
• Grid paths: $\binom{\text{total steps}}{\text{up steps}}$.

Steps

1. Build the triangle
2. Why the sums work
3. A board of pegs
4. The binomial theorem
5. Expand
6. Read the triangle
7. Grid paths