Resposta :
(n+2)(n+1)! - (n+1)! = 25/n(n-1)!
(n+2)(n+1)n(n-1)! - (n+1)n(n-1)! = 25/n(n-1)!
n(n-1)! . [(n+2)(n+1) - (n+1)] = 25/n(n-1)!
(n+2)(n+1) - (n+1) = 25
n²+n+2n+2-n-1 = 25
n²+2n+1-25=0
n²+2n-24=0
Δ = 2²-4.1.(-24)
Δ = 4+96
Δ = 100
n = (-2+/-√Δ)/2
n = (-2+/-\/100)/2
n = (-2+/-10)/2
n' = (-2+10)/2 = 4
n" = (-2-10)/2 = -6 (não convém)
S: n = 4