Question

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2011}\right)\)Tính nhanh

Giúp mik bài này nha! Mơn nhìu

Answer 1

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2011}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{2010}{2011}\)

\(=\frac{1}{2011}\)

Answer 2

\(\left(1-\begin{matrix}1\\2\end{matrix}\right)\) \(\left(\begin{matrix}1&-\begin{matrix}1\\3\end{matrix}\end{matrix}\right)\) \(\left(1-\begin{matrix}1\\4\end{matrix}\right)\) ... \(\left(1-\begin{matrix}1\\2011\end{matrix}\right)\)

= \(\frac{1}{2}\) x \(\frac{2}{3}\) x \(\frac{3}{4}\) x ... x \(\frac{2010}{2011}\)

= \(\frac{1.2.3....2010}{2.3.4....2011}\)

= \(\frac{1}{2011}\)