Question

Determinati numarul natural n,astfel incat:1/2 mai mic sau egal cun+1/n+2mai mic sau egal cu 2/3

Answer 1

1/2≤(n+1)/(n+2)≤2/3
1) 1/2≤(n+1)/(n+2)
n+2≤2(n+1)
n+2≤2n+2
n-2n≤2-2
-n≤0          inmultim -1
n≥0
n∈[0,+α)

2) (n+2)≤2/3
3(n+2)≤2
3n+6≤2
3n≤2-6
3n≤-4
n≤-4/3
n∈(-α,-4/3]
n∈(-α,-4/3]U[2,+α)