Question

Calcule o valor de:

(a) 15! · 4!/

13! · 3! (b) 21! − 3 · 20!/

19!

(c) 1/

(n + 1)! +

n − 1/

n

(d) n! − (n − 1)!/

(n − 1)! + (n − 2)!

Answer 1

Resposta:

Explicação passo-a-passo:

a) $\frac{15!.4!}{13!.3!}=\frac{15.14.13!.4.3!}{13!.3!}=\frac{15.14.4.13!.3!}{13!.3!}=15.14.4=840$

b) $\frac{21!-3.20!}{19!}=\frac{21.20!-3.20!}{19!}=\frac{20!(21-3)}{19!}=\frac{20.19!.18}{19!}=20.18=360$

c) Não dá pra entender,falta algum detalhe

d) $\frac{n!-(n-1)!}{(n-1)!+(n-2)!}=\frac{n(n-1)(n-2)!-(n-1)(n-2)!}{(n-1)(n-2)!+(n-2)!}=\frac{(n-2)![n(-1)-(n-1)]}{(n-2)![(n-1)+1]}=\frac{n(n-1)-(n-1)}{n-1+1}=\frac{n^{2}-n-n+1}{n}=\frac{n^{2}-2n+1}{n}$