Giải thích các bước giải:
Ta có :
$\dfrac{n}{n+1}<\dfrac{n+1}{n+2}$
$\to \dfrac 12<\dfrac 23$
$\dfrac 34<\dfrac 45$
.....
$\dfrac{99}{100}<\dfrac{100}{101}$
$\to A=\dfrac 12.\dfrac 34.\dfrac 56...\dfrac{99}{100}<\dfrac 23.\dfrac 45.\dfrac 67...\dfrac{100}{101}$
$\to A^2<\dfrac 12.\dfrac 34.\dfrac 56...\dfrac{99}{100}.\dfrac 23.\dfrac 45.\dfrac 67...\dfrac{100}{101}$
$\to A^2<\dfrac 12.\dfrac 23.\dfrac 34.\dfrac 45.\dfrac 56...\dfrac{99}{100}.\dfrac{100}{101}$
$\to A^2<\dfrac{1}{101}<\dfrac{1}{100}\to A<\dfrac{1}{10}$
Tương tự ta có :
$\dfrac{n}{n+1}<\dfrac{n+1}{n+2}$
$\to \dfrac 12>\dfrac 01$
$\dfrac 34>\dfrac 23$
.....
$\dfrac{99}{100}>\dfrac{98}{99}$
$\to A=\dfrac 12.\dfrac 34.\dfrac 56...\dfrac{99}{100}>\dfrac 12.\dfrac 23.\dfrac 45...\dfrac{98}{99}$
$\to A^2>\dfrac 12.\dfrac 12.\dfrac 23.\dfrac 34.\dfrac 45...\dfrac{98}{99}.\dfrac{99}{100}$
$\to A^2>\dfrac 12.\dfrac{1}{100}=\dfrac{1}{200}>\dfrac{1}{225}\to A>\dfrac{1}{15}$
