Đáp án:
\( - \dfrac{{6023}}{{2008}}\)
Giải thích các bước giải:
\(\begin{array}{l}
a. - \dfrac{1}{3} - \dfrac{2}{{11}} + \dfrac{1}{5} - \dfrac{5}{{13}} - \dfrac{{2007}}{{2008}} - \dfrac{{13}}{{15}} - \dfrac{{62}}{{143}}\\
= \left( { - \dfrac{1}{3} + \dfrac{1}{5} - \dfrac{{13}}{{15}}} \right) - \dfrac{2}{{11}} - \dfrac{5}{{13}} - \dfrac{{2007}}{{2008}} - \dfrac{{62}}{{143}}\\
= - 1 - \dfrac{2}{{11}} - \dfrac{5}{{13}} - \dfrac{{2007}}{{2008}} - \dfrac{{62}}{{143}}\\
= - \dfrac{{13}}{{11}} - \dfrac{5}{{13}} - \dfrac{{2007}}{{2008}} - \dfrac{{62}}{{143}}\\
= - \dfrac{{224}}{{143}} - \dfrac{{2007}}{{2008}} - \dfrac{{62}}{{143}}\\
= - 2 - \dfrac{{2007}}{{2008}}\\
= \dfrac{{ - 2.2008 - 2007}}{{2008}}\\
= - \dfrac{{6023}}{{2008}}
\end{array}\)
