Tìm x biết: x( 1/10.11 + 1/11.12 + 1/12.13 + 1/13.14 + 1/14.15) = 67,3

Lời giải:

\(x\left( {\frac{1}{{10.11}} + \frac{1}{{11.12}} + \frac{1}{{12.13}} + \frac{1}{{13.14}} + \frac{1}{{14.15}}} \right) = 67,3\)

\( \Leftrightarrow x\left( {\frac{1}{{10}} - \frac{1}{{11}} + \frac{1}{{11}} - \frac{1}{{12}} + \frac{1}{{12}} - \frac{1}{{13}} + \frac{1}{{13}} - \frac{1}{{14}} + \frac{1}{{14}} - \frac{1}{{15}}} \right) = 67,3\)

\(\begin{array}{l} \Leftrightarrow x\left( {\frac{1}{{10}} - \frac{1}{{15}}} \right) = 67,3 \Leftrightarrow x.\frac{1}{{30}} = 67,3\\ \Leftrightarrow x = 67,3:\frac{1}{{30}} \Leftrightarrow x = 2019\end{array}\)