(1-1\4)*(1-1/9)*(1-1/16)...(1-1/400)

Đáp án:

$\dfrac{21}{40}$.

Giải thích các bước giải:

$\left(1-\dfrac14\right)\!\!\left(1-\dfrac19\right)\!\!\left(1-\dfrac1{16}\right)\!.\!.\!.\!\left(1-\dfrac1{400}\right)\\=\dfrac34\!\cdot\!\dfrac89\!\cdot\!\dfrac{15}{16}\cdot\,.\!.\!.\cdot\dfrac{399}{400}\\=\dfrac{1.3}{2.2}\!\cdot\!\dfrac{2.4}{3.3}\!\cdot\!\dfrac{3.5}{4.4}\cdot\,.\!.\!.\cdot\dfrac{19.21}{20.20}\\=\dfrac{1.3.2.4.3.5...19.21}{2.2.3.3.4.4...20.20}\\=\dfrac{(1.2.3...19)(3.4.5...21)}{(2.3.4...20)(2.3.4...20)}\\=\dfrac{1.21}{20.2}\\=\dfrac{21}{40}$