Paskal üçburçlugy

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

Paskal üçburçlugy —Binomial koeffisientler we Paskal üçburçlugy şeýle bolsa,

$(x+y{)}^n=\sum _{k=0}^n(\genfrac{}{}{0ex}{}{n}{k})x^{n-k}{y}^k$

onda

$(\genfrac{}{}{0ex}{}{n}{k})=(\genfrac{}{}{0ex}{}{n-1}{k-1})+(\genfrac{}{}{0ex}{}{n-1}{k})$ bolar.

Formula

$(\genfrac{}{}{0ex}{}{n}{k})=\frac{n!}{k!\cdot (n-k)!}=\frac{n}{1}\cdot \frac{n-1}{2}\cdot \dots \cdot \frac{n-k+1}{k}$, $n,k\in {\mathbb{N}}_0$ bolsa

Meselem

$(\genfrac{}{}{0ex}{}{5}{3})=\frac{5!}{3!\cdot 2!}=\frac{5\cdot 4\cdot 3!}{2!\cdot 3!}=\frac{5\cdot 4}{2!}=\frac{20}{2}=10$