Question

21) resolva a equação (fatoriais)
(n+1)!+n!/ (n+2)!= 1/28

Answer 1

Resposta:

n! = 15/28

Explicação passo-a-passo:

$\frac{(n+1)!+n!}{(n+2)!} = \frac{1}{28}\\ \frac{n!+1!+n!}{n!+2!} = \frac{1}{28}\\\frac{2n!+1}{n!+2.1} = \frac{1}{28}\\28(2n!+1)=1(n!+2)\\\frac{28(2n!+1)}{(n!+2)}=1\\28(n!+\frac{1}{2}) =1\\28n! + \frac{28}{2}=1\\28n!+ 16=1\\n! = \frac{1-16}{28}\\ n! = \frac{15}{28}$

Att, Felipemlvr.