Bài tập 9.6 trang 24 SBT Toán 6 Tập 2

Bài tập 9.6 trang 24 SBT Toán 6 Tập 2

\(\begin{array}{l}
C = \frac{1}{2} + \frac{1}{{14}} + \frac{1}{{35}} + \frac{1}{{65}} + \frac{1}{{104}} + \frac{1}{{152}}\\
 = \frac{2}{4} + \frac{2}{{28}} + \frac{2}{{70}} + \frac{2}{{130}} + \frac{2}{{208}} + \frac{2}{{304}}\\
 = \frac{2}{{1.4}} + \frac{2}{{4.7}} + \frac{2}{{7.10}} + \frac{2}{{10.13}} + \frac{2}{{13.16}} + \frac{2}{{16.19}}\\
 = \frac{2}{3}\left( {\frac{3}{{1.4}} + \frac{3}{{4.7}} + \frac{3}{{7.10}} + \frac{3}{{10.13}} + \frac{3}{{13.16}} + \frac{3}{{16.19}}} \right)\\
 = \frac{2}{3}\left( {\frac{{4 - 1}}{{1.4}} + \frac{{7 - 4}}{{4.7}} + \frac{{10 - 7}}{{7.10}} + \frac{{13 - 10}}{{10.13}} + \frac{{16 - 13}}{{13.16}} + \frac{{19 - 16}}{{16.19}}} \right)\\
 = \frac{2}{3}\left( {1 - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + ... + \frac{1}{{16}} - \frac{1}{{19}}} \right)\\
 = \frac{2}{3}.\left( {1 - \frac{1}{{19}}} \right)\\
 = \frac{2}{3}.\frac{{18}}{{19}} = \frac{{12}}{{19}}
\end{array}\)

-- Mod Toán 6