Gọi C= 2/3 . 4/5 ...98/99

 => A.C = 1/2 . 2/3 . 3/4 ...  98/99 . 99/100

 => A.C = 1.2.3...99 / 2.3.4...100

 => A.C = 1/100 = 0,1

Mặt khác, ta thấy:

1/2<2/3

3/4<4/5

...........

97/98<98/99

=> A<C => A.A < C.A

              => A^2 < 0,1

             => A<0.1

Em tham khảo

$\text{A=$\dfrac{1}{2}$×$\dfrac{3}{4}$×.....$\dfrac{99}{100}$}$

$\text{Giả sử:B=$\dfrac{2}{3}$ ×$\dfrac{4}{5}$×......× $\dfrac{100}{101}$}$ 

$⇒A<B$

$⇒A²<A×B$

$\text{⇒A²<$\dfrac{1}{2}$>$\dfrac{2}{3}$ ×$\dfrac{3}{4}$×.....×$\dfrac{99}{100}$ ×$\dfrac{100}{101}$}$

$\text{⇒A²<$\dfrac{1}{101}$<$\dfrac{1}{100}$=($\dfrac{1}{10}$)²}$

$\text{⇒A²<($\dfrac{1}{10}$)²}$

$\text{⇒A<$\dfrac{1}{10}$=0,1}$

$\text{Vậy đpcm}$

$\text{Xin hay nhất}$