Question

1, tính :

\(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right)..........\left(\frac{1}{2004}-1\right)\left(\frac{1}{2005}-1\right)\)

2, tìm x \(\frac{4x}{2x-\frac{1}{5}}>0\)

Answer 1

\(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{2004}-1\right)\left(\frac{1}{2005}-1\right)\)

\(=\left(-\frac{1}{2}\right)\times\left(-\frac{2}{3}\right)\times...\times\left(-\frac{2003}{2004}\right)\times\left(-\frac{2004}{2005}\right)\)

\(=\frac{1}{2005}\)

***

\(\frac{4x}{2x-\frac{1}{5}}>0\)

\(\Leftrightarrow\begin{cases}4x>0\\2x-\frac{1}{5}>0\end{cases}\)

\(\Leftrightarrow\begin{cases}x>0\\x>\frac{1}{10}\end{cases}\)

\(\Leftrightarrow x>\frac{1}{10}\)