Cara Menghitung Pascal's Triangle
learn.whatIsHeading
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.
Panduan Langkah demi Langkah
- 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
Contoh Terpecahkan
Masukan
(x+y)^4
Hasil
1x⁴ + 4x³y + 6x²y² + 4xy³ + 1y⁴
Coefficients: Row 4 = 1,4,6,4,1
Masukan
Combinations C(5,2)
Hasil
10
Row 5, position 2 of Pascal's Triangle
Siap menghitung? Coba Kalkulator Pascal's Triangle gratis
Cobalah sendiri →