Question

Ma puteti ajuta la E7?

Answer 1

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
$n^{2}$+6n-40=0 => Δ=36+160=196
$n_{1,2} = \frac{-6+-14}{2} =\ \textgreater \ n_{1} = \frac{-6-14}{2}=-10$
$n_{2}= \frac{-6+14}{2} =4$

d)n!(n+1)(n+2) = 20n! | : n!
(n+1)(n+2)=20 => $n^{2}$+3n+2=20 => $n^{2} +3n-18=0$
Δ=9+72=81
[tex] n_{1,2} = \frac{-3+-9}{2} =\ \textgreater \ n_{1} = \frac{-3-9}{2} =-6 [/tex]$n_{2} = \frac{-3+9}{2} = 3$