Tính nhanh
\(\frac{1}{2} + \frac{{ - 1}}{3} + \frac{1}{4} + \frac{{ - 1}}{5} + \frac{1}{6} + \frac{{ - 1}}{7} + \frac{1}{8} + \frac{1}{7} + \frac{{ - 1}}{6} + \frac{1}{5} + \frac{{ - 1}}{4} + \frac{1}{3} + \frac{{ - 1}}{2}\)
Ta có:
\(\begin{array}{l}
\frac{1}{2} + \frac{{ - 1}}{3} + \frac{1}{4} + \frac{{ - 1}}{5} + \frac{1}{6} + \frac{{ - 1}}{7} + \frac{1}{8} + \frac{1}{7} + \frac{{ - 1}}{6} + \frac{1}{5} + \frac{{ - 1}}{4} + \frac{1}{3} + \frac{{ - 1}}{2}\\
= \left( {\frac{1}{2} + \frac{{ - 1}}{2}} \right) + \left( {\frac{1}{3} + \frac{{ - 1}}{3}} \right) + \left( {\frac{1}{4} + \frac{{ - 1}}{4}} \right) + \left( {\frac{1}{5} + \frac{{ - 1}}{5}} \right) + \left( {\frac{1}{6} + \frac{{ - 1}}{6}} \right) + \left( {\frac{1}{7} + \frac{{ - 1}}{7}} \right) + \frac{1}{8}\\
= 0 + 0 + 0 + 0 + 0 + 0 + \frac{1}{8}\\
= \frac{1}{8}
\end{array}\)
-- Mod Toán 6
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