Calculateur du Triangle de Pascal
Générez le triangle de Pascal et trouvez les coefficients binomiaux pour n'importe quelle ligne.
Binom
15
Row Sum64
Central20
Formule
Pascal's Triangle
Binomial Coefficient
C(n, k) = n! / (k! × (n-k)!)
This is the entry in row n, position k of Pascal's triangle (both starting from 0).
Properties
Exemple Résolu
Find the entry at row 6, position 2 of Pascal's triangle.
- 01C(6, 2) = 6! / (2! × 4!)
- 02= 720 / (2 × 24)
- 03= 720 / 48
- 04= 15
- 05Row 6: 1, 6, 15, 20, 15, 6, 1
Questions Fréquentes
What is Pascal's triangle?
Pascal's triangle is a triangular array where each entry is the sum of the two entries above it. Row n contains the binomial coefficients C(n,0) through C(n,n).
How is Pascal's triangle related to the binomial theorem?
The entries in row n give the coefficients when expanding (a+b)^n. For example, row 3 is 1,3,3,1, and (a+b)³ = a³ + 3a²b + 3ab² + b³.
What patterns exist in Pascal's triangle?
Column 0 is all 1s, column 1 gives natural numbers, column 2 gives triangular numbers. The triangle also contains Fibonacci numbers along certain diagonals.
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