Question

(ESPM - SP) Resolvendo a equação (n-1) = (n+1)!/30 obteremos n igual a:
a) 2
b) 3
c) 4
d) 5
e) 6

Answer 1

$(n-1)! = \dfrac{(n+1)!}{30} \\ \\ 30 = \dfrac{(n+1)!}{(n-1)!} \\ \\ \\ 30 = \dfrac{(n+1).n.(n-1)!}{(n-1)!} \\ \\ n^2 + n - 30 = 0 \\ \\ \Delta = 1 + 120 = 121 \\ \\ \\ x = \dfrac{-1+11}{2} = 10/2 = 5$

5, Alternativa 'D'