`text{Đáp án + Giải thích các bước giải}`
Đặt `A=1/4+1/9+1/16+...+1/81+1/100`
`=>A=1/4+1/9+1/16+...+1/81+1/100`
`=>A=1/(2.2)+1/(3.3)+1/(4.4)+...+1/(9.9)+1/(10.10)`
`text{Ta thấy:}`
$\begin{cases} \dfrac{1}{2.2}<\dfrac{1}{1.2}\\\dfrac{1}{3.3}<\dfrac{1}{2.3}\\\dfrac{1}{4.4}<\dfrac{1}{3.4}\\...\\\dfrac{1}{9.9}<\dfrac{1}{8.9}\\\dfrac{1}{10.10}<\dfrac{1}{9.10}\end{cases}$
`=>A=1/(2.2)+1/(3.3)+1/(4.4)+...+1/(9.9)+1/(10.10)<1/(1.2)+1/(2.3)+1/(3.4)+...+1/(8.9)+1/(9.10)`
`=>A<1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9+1/9-1/10`
`=>A<1-1/10=9/10`
Vậy `A<9/10`
