Đáp án:
$a)-\dfrac{1006}{1007}\\
b)-7$
Giải thích các bước giải:
$a)\dfrac{1}{2014}-\dfrac{1}{2014.2013}-\dfrac{1}{2013.2012}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\\
=-\left ( -\dfrac{1}{2014}+\dfrac{1}{2014.2013}+\dfrac{1}{2013.2012}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1} \right )\\
=-\left ( \dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2012.2013}+\dfrac{1}{2013.2014}-\dfrac{1}{2014} \right )\\
=-\left ( 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2012}-\dfrac{1}{2013}+\dfrac{1}{2013}-\dfrac{1}{2014}-\dfrac{1}{2014} \right )\\
=-\left ( 1-\dfrac{2}{2014} \right )\\
=-\left ( 1-\dfrac{1}{1007} \right )\\
=-\left ( \dfrac{1007}{1007}-\dfrac{1}{1007} \right )\\
=-\dfrac{1006}{1007}\\
b)\left ( 8\dfrac{-9}{4}+\dfrac{2}{7} \right )-\left ( -6-\dfrac{3}{7}+\dfrac{5}{4} \right )-\left ( 3+\dfrac{2}{4}-\dfrac{9}{7} \right )\\
= \dfrac{-41}{4}+\dfrac{2}{7} +6+\dfrac{3}{7}-\dfrac{5}{4}- 3-\dfrac{2}{4}+\dfrac{9}{7} \\
= \left (\dfrac{-41}{4} -\dfrac{5}{4} -\dfrac{2}{4}\right )+\left (\dfrac{2}{7} +\dfrac{9}{7}+\dfrac{3}{7} \right )+6- 3\\
=\dfrac{-48}{4}+\dfrac{14}{7}+3\\
=-12+2+3\\
=-7$
