Đáp án:
`1/2^2+1/3^2+1/4^2+...+1/100^2<3/4`
Giải thích các bước giải:
`A=1/2^2+1/3^2+1/4^2+...+1/100^2`
`=>A=1/4+1/3.3+1/4.4+...+1/100.100`
`=>A<1/4+1/2.3+1/3.4+...+1/99.100`
`=>A<1/4+1/2-1/3+1/3-1/4+...+1/99-1/100`
`=>A<1/4+1/2-1/100`
`=>A<1/4+49/100`
`=>A<25/100+49/100`
`=>A<74/100<75/100=3/4`
`=>A<3/4`
Vậy `1/2^2+1/3^2+1/4^2+...+1/100^2<3/4`.