Đáp án:
`1/3^2+1/4^2+1/5^2+....+1/100^2`
Ta cóa:
`1/3^2<1/(2.3)`
`1/4^2<1/(3.4)`
`.....`
`1/100^2<1/(99.100)`
`-> 1/3^2+1/4^2+1/5^2+....+1/100^2<1/(2.3)+1/(3.4)+....+1/(99.100)`
`=1/2-1/3+1/3-1/4+...+1/99-1/100`
`=1/2-1/100`
`-> 1/3^2+1/4^2+1/5^2+....+1/100^2<1/2 (đpcm)`