a) 3(n+1)!=(n+1)!(n+2) | :(n+1)!
3=n+2 =) 3-2=n => n=1
b) (n+1)!(n+1) = 6(n+1)!(n+2) | : (n+1)!
n+1=6(n+2) => n+1=6n+12 => n-6n=12-1 => -5n=11 => n=-11/5
c) 5(n-1)!n+(n-1)!n(n+1)=40(n-1)! | :(n-1)!
5n+n(n+1) = 40
[tex] n^{2} [/tex]+6n-40=0 => Δ=36+160=196
[tex] n_{1,2} = \frac{-6+-14}{2} =\ \textgreater \ n_{1} = \frac{-6-14}{2}=-10[/tex]
[tex] n_{2}= \frac{-6+14}{2} =4[/tex]
d)n!(n+1)(n+2) = 20n! | : n!
(n+1)(n+2)=20 => [tex] n^{2} [/tex]+3n+2=20 => [tex] n^{2} +3n-18=0[/tex]
Δ=9+72=81
[tex] n_{1,2} = \frac{-3+-9}{2} =\ \textgreater \ n_{1} = \frac{-3-9}{2} =-6
[/tex][tex] n_{2} = \frac{-3+9}{2} = 3 [/tex]
