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Pascal's Triangle is a triangular array where each number is the sum of the two numbers directly above it. It encodes binomial coefficients, combinatorics, and the coefficients of binomial expansions. Named after Blaise Pascal (1623–1662) though known much earlier.
Stapsgewijze handleiding
- 1Row 0: 1 | Row 1: 1, 1 | Row 2: 1, 2, 1 | Row 3: 1, 3, 3, 1
- 2Entry C(n,k) = entry in row n, position k = n! / (k!(n−k)!)
- 3Binomial expansion: (a+b)^n coefficients are row n of the triangle
- 4Sum of row n = 2^n; diagonal sums give Fibonacci numbers
Uitgewerkte voorbeelden
Invoer
(x+y)^4
Resultaat
1x⁴ + 4x³y + 6x²y² + 4xy³ + 1y⁴
Coefficients: Row 4 = 1,4,6,4,1
Invoer
Combinations C(5,2)
Resultaat
10
Row 5, position 2 of Pascal's Triangle
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