Question

Tính:
A = (1 - 1/10) : (1 + 1/10) : (1 + 1/11) : (1 + 1/12) : ... : (1 + 1/500)

Answer 1

\(A=\left(1-\dfrac{1}{10}\right):\left(1+\dfrac{1}{10}\right):\left(1+\dfrac{1}{11}\right):\left(1+\dfrac{1}{12}\right):...:\left(1+\dfrac{1}{500}\right)\)
\(=\dfrac{9}{10}:\dfrac{11}{10}:\dfrac{12}{11}:\dfrac{13}{12}:...:\dfrac{501}{500}\)
\(=\dfrac{9}{10}\cdot\dfrac{10}{11}\cdot\dfrac{11}{12}\cdot\dfrac{12}{13}\cdot....\cdot\dfrac{500}{501}\)
\(=\dfrac{9}{501}=\dfrac{3}{167}\)