Pascal's Triangle Calculator
Generate the first N rows of Pascal's triangle. Each entry equals the sum of the two entries above it.
How to Use the Pascal's Triangle Calculator
- Enter the number of rows you want (1–20).
- Click Generate to see the triangle.
- Each row shows the binomial coefficients for that level.
Riferimento Rapido
| Da | A |
|---|---|
| Row 0 | 1 |
| Row 4 | 1, 4, 6, 4, 1 |
| Row 6 | 1, 6, 15, 20, 15, 6, 1 |
| Row 10 sum | 1024 (2^10) |
| Row n sum | 2^n |
Casi d'Uso
- •Studying binomial coefficients in combinatorics class.
- •Visualizing patterns in Pascal's triangle.
- •Computing binomial expansion coefficients quickly.
Formula
C(n, k) = C(n−1, k−1) + C(n−1, k), with C(n, 0) = C(n, n) = 1. Maximum 20 rows.
Domande Frequenti
What is Pascal's triangle?
A triangular array where each number is the sum of the two numbers directly above it. Row n contains the binomial coefficients C(n, k).
What is the maximum number of rows?
This calculator supports up to 20 rows to keep the output readable.
How is it used?
In combinatorics, probability, algebra (binomial expansion), and fractal patterns (Sierpinski triangle).