`A=8/9+24/25+48/49+.....+10200/10201`

`A=(1-1/9)+(1-1/25)+(1-1/49)+(1-1/10201)`

`A=(1+1+1+...+1)-(1/9+1/25+1/49+...+1/10201`)

`A=50-(1/3^2+1/5^2+1/7^2+...+1/101^2)`

Đặt `B=1/3^2+1/5^2+1/7^2+....+1/101^2`

Ta có:

`1/3^2=1/9<1/(2×4)`

`1/5^2=1/25<1/(4×6)`

`1/7^2=1/49<1/(6×8)`

....

`1/101^2=1/10201<1/(100×102)`

`⇒` `B<1/(2×4)+1/(4×6)+1/(6×8)+...+1/(100×102)`

`B< 2×[1/(2×4)+1/(4×6)+1/(6×8)+....+1/(100×102)]`

`B< 2/(2×4)+2/(4×6)+2/(6×8)+....+2/(100×102):2`

`B<(1/2-1/102):2`

`B<25/102<1/4(0,25)`

`⇒` `B<1/4`

`⇒` `A>49,75`