Tìm x biết \(\frac{x}{{2008}} - \frac{1}{{10}} - \frac{1}{{15}} - \frac{1}{{21}} - \ldots - \frac{1}{{120}} = \frac{5}{8}\)
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Lời giải:
Báo sai\(\begin{array}{l} \frac{x}{{2008}} - \frac{1}{{10}} - \frac{1}{{15}} - \frac{1}{{21}} - \ldots - \frac{1}{{120}} = \frac{5}{8}\\ \Leftrightarrow \frac{x}{{2008}} - \left( {\frac{2}{{20}} + \frac{2}{{30}} + \frac{2}{{42}} + \ldots + \frac{2}{{240}}} \right) = \frac{5}{8}\\ \Leftrightarrow \frac{x}{{2008}} - \left( {\frac{2}{{4.5}} + \frac{2}{{5.6}} + \frac{2}{{6.7}} + \ldots + \frac{2}{{15.16}}} \right) = \frac{5}{8}\\ \Leftrightarrow \frac{x}{{2008}} - \left( {\frac{1}{4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6} \ldots + \frac{1}{{15}} - \frac{1}{{16}}} \right) \cdot 2 = \frac{5}{8}\\ \Leftrightarrow \frac{x}{{2008}} - \left( {\frac{1}{4} - \frac{1}{{16}}} \right) \cdot 2 = \frac{5}{8}\\ \Leftrightarrow \frac{x}{{2008}} - \frac{3}{8} = \frac{5}{8} \Leftrightarrow \frac{x}{{2008}} = 1 \Leftrightarrow x = 2008 \end{array}\)