Question

Hey! Va rog sa ma ajutati la exercitiul 4 punctele a si b

Answer 1

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: