`B= 1/2^2 + 1/3^2 + 1/4^2 +...+ 1/99^2 + 1/100^2`
$\text{Ta có:}$
`1/2^2 < 1/(1.2)`
`1/3^2 < 1/(2.3)`
`1/4^2 < 1/(3.4)`
`...`
`1/100^2 < 1/(99.100)`
`=> B < 1/(1.2) + 1/(2.3) +...+ 1/(99.100)`
`=> B < 1/1 - 1/2 + 1/2 - 1/3 +...+ 1/99 - 1/100`
`=> B < 1/1 - 1/100`
`=> B < 100/100 - 1/100`
`=> B < 99/100`
mà ` 99/100 <1`
`=> B<1 (đpcm)`
~ Học tốt ~