Paskal üçburçlugy

Paskal üçburçlugyň ilkinji 15 setiri (n = 0, 1, …, 14)

Binomial koeffisientler we Paskal üçburçlugy şeýle bolsa,

$(x+y)^n=\sum_{k=0}^n{n \choose k}x^{n-k}y^{k}$

onda

${n \choose k} = {n-1 \choose k-1} + {n-1 \choose k}$ bolar.

Formula

${n \choose k} = \frac{n!}{k!\cdot (n-k)!} = \frac n 1 \cdot \frac{n-1}{2}\cdot\ldots\cdot \frac{n-k+1}{k}$, $n, k\in\N_0$ bolsa

Meselem

${5 \choose 3} = \frac{5!}{3! \cdot 2!} = \frac{5\cdot 4\cdot 3!}{2!\cdot 3!} = \frac{5\cdot 4}{2!} = \frac{20}{2} = 10$