Chứng minh 1/2^2 + 1/3^2+ 1/4^2 +... + 1/2022^2 < 1
Giải thích
Ta có: 122<11.2; 132<12.3; 142<13.4;...; 120212<12020.2021
Đặt A=122+132+142+...+120222
⇒A=122+132+142+...+120222<11.2+12.3+13.4+...+12020.2021⇒A<1−12+12−13+13−14+...+12020−12021⇒A<1−12021⇒A<20202021
Vì 2020 < 2021 nên 20202021<1
Do đó A<20202021<1.
Vậy 122+132+142+...+120222<1 (đpcm).