Question

cat de rapid posibil! ms​

Answer 1

a) 1/10 < 1/n²

n² < 10

n < ±√10

Dar n este numar natural deci e doar varianta n < √10

n = {0, 1, 2, 3}

b) (n+2)/3 </ 5/3 ai acelasi numitor asa ca nu mai e necesar sa-l scrii

n+2 </ 5

n </ 3

n = {0, 1, 2, 3}

c) 4/17 </ n²/17 < 25/17

4 </ n² < 25 ridici la radical relatia

2 </ n < 5

n = {2, 3, 4}

d) 12/8 > 12/(n+5)

12(n+5) > 96

n+5 > 8

n > 3, n apartine (3, infinit)

12/(n+5) >/ 12/20

12(n+5) >/ 240

n+5 >/ 20

n >/ 15, n apartine [15, infinit)

Verificand ambele cazuri n poate lua valori incepand cu intervalul [15, infinit)