Question

Touu desesperada socorro eu não foi conseguindo fazer preciso de ajuda???

Answer 1

1-

a) 2! + 4!=2.1+4.3.2.1=2+24=26

b) 5! - 3!=5.4.3.2.1 + 3.2.1 = 120 + 6=126

c) 0!+3!=1 + 3.2.1=1+6=7

d) 4!+5!=4.3.2.1+5.4.3.2.1=24+120=144

2-

a)

$\frac{4!}{3!}=\frac{4.3!}{3!}=4$

b)

$\frac{6!}{4!}=\frac{6.5.4!}{4!}=6.5=30$

c)

$\frac{11!}{9!}=\frac{11.10.9!}{9!}=11.10=110$

d)

$\frac{8!5!}{6!9!}=\frac{8!.5!}{6.5!.9.8!}=\frac{1}{6.9}=\frac{1}{54}$

3-

a)

$\frac{x!}{(x-1)!}=8\\\\ \frac{x(x-1)!}{(x-1)!}=8\\\\ x=8$

b)

$\frac{(n+1)!}{n!}=7\\\\ \frac{(n+1).(n)!}{n!}=7\\\\ n+1=7\\ n=7-1\\ n=6$

c)

$\frac{(n-2)!}{(n-3)!}=10\\\\ \frac{(n-2).(n-3)!}{(n-3)!}=10\\\\ n-2=10\\ n=10+2\\ n=12$

d)

$\frac{(x+2)!}{2(x-6)!}=\frac{(x+1)!}{(x-7)!}\\\\ \frac{(x+2)!}{2(x+1)!}=\frac{(x-6)!}{(x-7)!}\\\\ \frac{(x+2)(x+1)!}{2(x+1)!}=\frac{(x-6)(x-7)!}{(x-7)!}\\\\ \frac{(x+2)}{2}=(x-6)\\\\ (x+2)=2.(x-6)\\ x+2=2x-12\\ x-2x=-12-2\\ -x=-14\\ x=14$

3- (novamente,rsrs)

$\frac{(n-1)!+n!}{(n-1)!}=\frac{(n-1)!+(n)(n-1)!}{(n-1)!}=1+n=$

4-

$\frac{(n+4)!}{(n^2+7n+12)n!}=\frac{(n+4)(n+3)(n+2)(n+1)n!}{(n^2+7n+12)n!}=\\\\ =\frac{(n+4)(n+3)(n+2)(n+1)}{(n^2+7n+12)}=\\\\ =\frac{(n+4)(n+3)(n+2)(n+1)}{(n+3)(n+4)}=\\\\ =(n+2)(n+1)=n^2+n+2n+2=n^2+3n+2$

5-

$\frac{9!}{7!}-\frac{8!}{6!}=\frac{9.8.7!}{7!}-\frac{8.7.6!}{6!}=\\\\ =9.8-8.7=8.(9-7)=8.2=16$

Letra B

6-

01. Falsa, pois 0!=1

02. Verdadeira, pois

$\frac{6!}{4!}=\frac{6.5.4!}{4!}=6.5=30$

04. Verdadeira, pois 6!=6.5!

08. Verdadeira, pois n!=n.(n-1)!

16. Verdadeira, pois

$\frac{n!}{(n-1)!}=\frac{n(n-1)!}{(n-1)!}=n$

32. Verdadeira, pois 9!=9.8.7!

Resposta: 62