Question

[Moon]

tìm tích rồi tìm số nghịch đảo của chúng

T=(1- \(\dfrac{1}{3}\) )(1-  \(\dfrac{1}{5}\))(1-\(\dfrac{1}{7}\)  )(1- \(\dfrac{1}{9}\) )(1- \(\dfrac{1}{11}\) )(1-  \(\dfrac{1}{2}\))(1-  \(\dfrac{1}{4}\))(1-  \(\dfrac{1}{6}\))(1-  \(\dfrac{1}{8}\))(1- \(\dfrac{1}{10}\) )

Answer 1

[Nguyễn Lê Phước Thịnh]

Ta có: \(P=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{11}\right)\)

\(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-9}{10}\cdot\dfrac{-10}{11}\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{9}{10}\cdot\dfrac{10}{11}\)

\(=\dfrac{1}{11}\)