Giải thích các bước giải:
Ta có:
$A=\dfrac12.\dfrac34.\dfrac56.\dfrac78....\dfrac{79}{80}$
$\to A<\dfrac23.\dfrac45.\dfrac67....\dfrac{90}{81}$
$\to A^2=(\dfrac12.\dfrac34.\dfrac56.\dfrac78....\dfrac{79}{80}).(\dfrac12.\dfrac34.\dfrac56.\dfrac78....\dfrac{79}{80})$
$\to A^2<(\dfrac12.\dfrac34.\dfrac56.\dfrac78....\dfrac{79}{80}).(\dfrac23.\dfrac45.\dfrac67....\dfrac{80}{81})$
$\to A^2<\dfrac12.\dfrac23.\dfrac34.\dfrac45.\dfrac56.\dfrac67...\dfrac{80}{81}$
$\to A^2<\dfrac1{81}$
$\to A<\dfrac19$
