Question

Aratati ca: a)daca a b) 3/4<1/3+1/4+1/5+1/6+1/7+1/8<2

Answer 1

 1/3≤1/3
1/4<1/3
1/5<1/3
1/6<1/3
1/7<1/3
1/8<1/3
Adunam inegalitatile de mai sus:
1/3+1/4+1/5+1/6+1/7+1/8<1/3+1/3+1/3+1/3+1/3+1/3
1/3+1/4+1/5+1/6+1/7+1/8<6/3
1/3+1/4+1/5+1/6+1/7+1/8<2(1)
Procedeul descris mai sus se numeste majorare. Acum vom face o minorare.
1/8<1/3
1/8<1/4
1/8<1/5
1/8<1/6
1/8<1/7
1/8≤1/8
Adunam inegalitatile de mai sus:
1/8+1/8+1/8+1/8+1/8+1/8<1/3+1/4+1/5+1/6+1/7+1/8
6/8<1/3+1/4+1/5+1/6+1/7+1/8
3/4<1/3+1/4+1/5+1/6+1/7+1/8(2)
Din (1)+(2)=> 3/4<1/3+1/4+1/5+1/6+1/7+1/8<2