Giải thích các bước giải:
Áp dụng bài toán cho phân số $\dfrac{a}{b}<1\to \dfrac{a}{b}<\dfrac{a+n}{b+n}$
Ta có:
$\dfrac12<\dfrac{1+1}{2+1}=\dfrac23$
$\dfrac34<\dfrac{3+1}{4+1}=\dfrac45$
$...$
$\dfrac{199}{200}<\dfrac{199+1}{200+1}=\dfrac{200}{201}$
Lại có:
$C=\dfrac12.\dfrac34.\dfrac56....\dfrac{199}{200}$
$\to C^2=(\dfrac12.\dfrac34.\dfrac56....\dfrac{199}{200}).(\dfrac12.\dfrac34.\dfrac56....\dfrac{199}{200})$
$\to C^2<(\dfrac12.\dfrac34.\dfrac56....\dfrac{199}{200}).(\dfrac23.\dfrac45.\dfrac67....\dfrac{200}{201})$
$\to C^2<\dfrac{1.2.3...200}{2.3.4....201}$
$\to C^2<\dfrac1{201}$
