Đáp án:
$A = \dfrac{9}{100}$
Giải thích các bước giải:
$\begin{array}{l}A = \left(\dfrac{1}{10} -1\right)\left(\dfrac{1}{11} -1\right)\left(\dfrac{1}{12} -1\right)\cdots\left(\dfrac{1}{99} -1\right)\left(\dfrac{1}{100} -1\right) \\ \to A = \left(\dfrac{1}{10} -\dfrac{10}{10}\right)\left(\dfrac{1}{11} -\dfrac{11}{11}\right)\left(\dfrac{1}{12} -\dfrac{12}{12}\right)\cdots\left(\dfrac{1}{99} -\dfrac{99}{99}\right)\left(\dfrac{1}{100} -\dfrac{100}{100}\right)\\ \to A = \left(-\dfrac{9}{10}\right)\left(-\dfrac{10}{11}\right)\left(-\dfrac{11}{12}\right)\cdots\left(-\dfrac{98}{99}\right)\left(-\dfrac{99}{100}\right)\\ \to A = \dfrac{9}{100}\end{array}$
