`1/3^2+1/4^2+1/5^2+...+1/100^2 < 1/(2.3)+1/(3.4)+1/(4.5)+...+1/(99.100)`
Đặt `A=1/(2.3)+1/(3.4)+1/(4.5)+...+1/(99.100)`
`⇒A=1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100`
`⇒A=1/2-1/100`
`⇒A<1/2`
mà `1/3^2+1/4^2+1/5^2+...+1/100^2 <A`
`⇒1/3^2+1/4^2+1/5^2+...+1/100^2 <1/2`