Bài 1:
\(\left( { - 1{1 \over 3}} \right).\left( { - 1{1 \over 4}} \right).\left( { - 1{1 \over 5}} \right)...\left( { - 1{1 \over {2012}}} \right)\)
\(\eqalign{ & = {4 \over { - 3}}.{{ - 5} \over 4}.{6 \over { - 5}}...{{ - 2013} \over {2012}} \cr & = {4 \over { - 3}}.{{ - 5} \over 4}.{6 \over { - 5}}...{{ - 2013} \over {2012}} \cr & = {{ - 2013} \over { - 3}} = {{2013} \over 3}. \cr} \)
Bài 2: Ta thấy \(\left( {x + 1} \right)\left( {x - 3} \right) < 0\) khi \(x + 1\) và \(x - 3\) trái dấu.
Trường hợp 1:
\(\left\{ \matrix{ x + 1 > 0 \hfill \cr x - 3 < 0 \hfill \cr} \right. \Rightarrow \left\{ \matrix{ x > - 1 \hfill \cr x < 3 \hfill \cr} \right. \)\(\;\Rightarrow - 1 < x < 3\)
Trường hợp 2:
\(\left\{ \matrix{ x + 1 > 0 \hfill \cr x - 3 > 0 \hfill \cr} \right. \Rightarrow \left\{ \matrix{ x < - 1 \hfill \cr x > - 3 \hfill \cr} \right. \Rightarrow x \in \emptyset \)
Vậy để \(\left( {x + 1} \right)\left( {x - 3} \right) < 0\) thì \( - 1 < x < 3.\)
