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Đáp án:

$A=\dfrac{40}{21}$

Giải thích các bước giải:

$A=\dfrac{2^2}{1.3}\cdot\dfrac{3^2}{2.4}\cdot\dfrac{4^2}{3.5} \ \cdot\,.\!.\!.\cdot\ \dfrac{20^2}{19.21}\\\Rightarrow A=\dfrac{2.2}{1.3}\cdot\dfrac{3.3}{2.4}\cdot\dfrac{4.4}{3.5}\ \cdot\,.\!.\!.\cdot\ \dfrac{20.20}{19.21}\\\Rightarrow A=\dfrac{(2.3.4...20).\!(2.3.4...20)}{(1.2.3...19).\!(3.4.5...21)}\\\Rightarrow A=\dfrac{20.2}{1.21}=\dfrac{40}{21}$