3. Tính $\left ( 1-\frac{1}{2} \right ).\left ( 1-\frac{1}{3} \right ).\left ( 1-\frac{1}{4} \right ).....\left ( 1-\frac{1}{2010} \right )$
4. Tìm x biết:
a) $\frac{-12}{7}.\left ( \frac{3}{4}-x \right ).\frac{1}{4}=0$
b) $x : \frac{17}{18}=\frac{-2}{5}.\frac{-9}{17}$
5. Tính biểu thức : $\frac{4}{3.5} + \frac{4}{5.7} + \frac{4}{7.9} + \frac{4}{9.11}$ bằng cách hợp lí nhất.
Bài Làm:
3. $\left ( 1-\frac{1}{2} \right ).\left ( 1-\frac{1}{3} \right ).\left ( 1-\frac{1}{4} \right ).....\left ( 1-\frac{1}{2010} \right )$
= $\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2009}{2010}$
= $\frac{1.2.3.....2009}{2.3.4.....2010}$
= $\frac{1}{2010}$
4.
a) $\frac{-12}{7}.\left ( \frac{3}{4}-x \right ).\frac{1}{4}=0$
$\Leftrightarrow \frac{3}{4}-x=0$
$\Leftrightarrow x=\frac{3}{4}$
b) $x : \frac{17}{18}=\frac{-2}{5}.\frac{-9}{17}$
$\Leftrightarrow x : \frac{17}{18}=\frac{18}{85}$
$\Leftrightarrow x = \frac{18}{85}.\frac{17}{18}$
$\Leftrightarrow x = \frac{17}{85}$
$\Leftrightarrow x = \frac{1}{5}$
5. Ta có:
$\frac{4}{3.5} + \frac{4}{5.7} + \frac{4}{7.9} + \frac{4}{9.11}$
= 2.$\left ( \frac{2}{3.5} + \frac{2}{5.7} + \frac{2}{7.9} + \frac{2}{9.11} \right )$
= 2.$\left ( \frac{5-3}{3.5} + \frac{7-5}{5.7} + \frac{9-7}{7.9} + \frac{11-9}{9.11} \right )$
= 2.$\left ( \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7}+\frac{1}{7} - \frac{1}{9} + \frac{1}{9} - \frac{1}{11} \right )$
= $2.\left ( \frac{1}{3}-\frac{1}{11} \right )$
= $2.\frac{8}{33}$
= $\frac{16}{33}$