Question

2/5 <1/2^2+1/3^2+1/4^2+...+1/9^2 <8/9 ^înseamnă putere

Answer 1

2/5<1/2²+1/3²+1/4²+...+1/9²<8/9
1/2·3<1/2²<1/1·2
1/3·4<1/3²<1/2·3
1/4·5<1/4²<1/3·4
.....
1/9·10<1/9²<1/8·9
Adunand relatiile vom obtine
1/2·3+1/3·4+1/4·5+...+1/9·10<1/2²+1/3²+1/4²+...+1/9²<8/9
1/2-1/10<1/2²+1/3²+1/4²+...+1/9²<8/9
4/10<1/2²+1/3²+1/4²+...+1/9²<8/9
Dar 4/10=2/5
In concluzie
2/5<1/2²+1/3²+1/4²+...+1/9²<8/9