Răspuns:
(n-1)!/(n-3)!<72
(n-3)!*(n-2)(n-1)/(n-3)!<72
n-2)(n-1)<72
n²-2n-n+2<72
n²-3n+2-72<0
n²-3n-70<0
Ecuatia atasata
n²-3n-70=0
Δ=3²-4*(-70)=9+280=289
√Δ=17
n1=(3-17)/2= -7
n2=(3+17)/2=10
n∈(-7,10)∩N={0,1,2,...9}
b)(n+2)/(n+1)(n+2)<1000
n!(n+1)(n+2)/(n+1)(n+2)<1000
n!<1000
6!=1*2*,,,*6=720<1000
7!=720*7>1000=>
Inecuatia este adevarata pt n!=6!=>
n={0,1,2...6}
Explicație pas cu pas:
