Pascal's Triangle Row Calculator
Calculate specific entries from Pascal's triangle. Find C(n, k) - the binomial coefficient - for any row n and position k.
Binom
15
Formula
## 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 - Each entry equals the sum of the two entries above it - Row sums: each row sums to 2^n - Symmetry: C(n, k) = C(n, n-k) - The entries give the coefficients of (a+b)^n
Esempio Risolto
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
Domande Frequenti
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.
Impara