Đáp án:

Giải thích các bước giải:

Xét:

`1/3^2<1/(2.4)=1/2(1/2-1/4)`

`1/5^2<1/(4.6)=1/2(1/4-1/6)`

`1/7^2<1/(6.8)=1/2(1/6-1/8)`

`...`

`1/2025^2<1/(2024.2026)=1/2(1/2024-1/2026)`

`=>1/3^2+1/5^2+1/7^2+...+1/2025^2<1/2(1/2-1/4)+1/2(1/4-1/6)+1/2(1/6-1/8)+...+1/2(1/2024-1/2026)`

`=>1/2A<1/2(1/2-1/4)+1/2(1/4-1/6)+1/2(1/6-1/8)+...+1/2(1/2024-1/2026)`

`=>1/2A<1/2(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2024-1/2026)`

`=>1/2A<1/2(1/2-1/2026)`

`=>A<1/2-1/2026`

`=>A<1012/2026`

`=>A<506/1013(đpcm)`