Đáp án: x=20,8 hoặc x=-19,2
Giải thích các bước giải:
$\begin{array}{l}
\frac{4}{{1.5}} + \frac{4}{{5.9}} + ... + \frac{4}{{97.101}} = \left| {\frac{{5x - 4}}{{101}}} \right|\\
\Rightarrow \frac{{5 - 1}}{{1.5}} + \frac{{9 - 5}}{{5.9}} + ... + \frac{{101 - 97}}{{97.101}} = \frac{{\left| {5x - 4} \right|}}{{101}}\\
\Rightarrow 1 - \frac{1}{5} + \frac{1}{5} - \frac{1}{9} + ... + \frac{1}{{97}} - \frac{1}{{101}} = \frac{{\left| {5x - 4} \right|}}{{101}}\\
\Rightarrow 1 - \frac{1}{{101}} = \frac{{\left| {5x - 4} \right|}}{{101}}\\
\Rightarrow \frac{{101 - 1}}{{101}} = \frac{{\left| {5x - 4} \right|}}{{101}}\\
\Rightarrow 100 = \left| {5x - 4} \right|\\
\Rightarrow \left[ \begin{array}{l}
5x - 4 = 100\\
5x - 4 = - 100
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
5x = 104\\
5x = - 96
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 20,8\\
x = - 19,2
\end{array} \right.
\end{array}$
