Question

Questão de álgebra- Binômio de Newton/Triângulo de Pascal:
     Resolva a equação:

Answer 1

$\dbinom{16}{0}=1$

$\dbinom{17}{1}=17$

$\dbinom{18}{2}=\dfrac{18\cdot17}{2}=153$

$\dbinom{19}{3}=\dfrac{19\cdot18\cdot17}{3!}=969$

$\dbinom{20}{4}=\dfrac{20\cdot19\cdot18\cdot17}{4!}=4845$

$\dbinom{21}{5}=\dfrac{21\cdot20\cdot19\cdot18\cdot17}{5!}=20349$


$1+17+153+969+4845+20349=\dbinom{22}{x-3}$

$26~334=\dbinom{22}{x-3}$

Lembre-se que, $\dbinom{n}{p}=\dbinom{n}{n-p}$.

Veja que, $\dbinom{22}{5}=\dbinom{22}{17}=26~334$.

Assim, $x-3=5$ ou $x-3=17$. Logo, $x=8$ ou $x=20$.