Question

simplifique:
A) 15!+3*14!-13!/13!

B) 203!+204!/203!

Answer 1

a) $\frac{15!+3 \cdot 14!-13!}{13!}$

Vamos simplificar chegando no menor fatorial, que é 13!. Olha no exemplo:

$5! = 5 \cdot \underbrace{4 \cdot 3 \cdot 2 \cdot 1}_{4!} \\\\\ \therefore 5! = 5\cdot 4!$

Vamos simplificar usando esta ideia

$\frac{15!+3 \cdot 14!-13!}{13!} \\\\ \frac{15 \cdot 14 \cdot 13!+3 \cdot 14 \cdot 13!-13!}{13!} \\\\ termo \ comum: 13! \Rightarrow vamos \ fatora-lo \\\\ \frac{13! (15\cdot 14+3 \cdot 14-1)}{13!} \\\\ anula \ 13! \\\\ (15 \cdot 14) + (3 \cdot 14) - 1 \\\\ 210 + 42-1 = \boxed{\boxed{251}}$



b) $\frac{203! +204!}{203!} \\\\ \frac{203! +204 \cdot 203!}{203!} \\\\ \frac{203! (204+1)}{203!} \\\\ anulando \\\\ 204 + 1 = \boxed{\boxed{205}}$