\(\left|x+\frac{1}{1.2}\right|+\left|x+\frac{1}{2.3}\right|+\left|x+\frac{1}{3.4}\right|+.............+\left|x+\frac{1}{99.100}\right|=100x^{\left(1\right)}\)
Ta có \(\left|x+\frac{1}{1.2}\right|\ge0;\left|x+\frac{1}{2.3}\right|\ge0;\left|x+\frac{1}{3.4}\right|\ge0;...........;\left|x+\frac{1}{99.100}\right|\ge0\)
\(\Rightarrow VT\ge0\Rightarrow VP\ge0\Rightarrow100x\ge0\Rightarrow x\ge0\)
Với \(x\ge0\).Từ (1) \(\Rightarrow x+\frac{1}{1.2}+x+\frac{1}{2.3}+x+\frac{1}{3.4}+.................+x+\frac{1}{99.100}=100x\)
\(\Rightarrow\left(x+x+x+.......+x\right)+\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+............+\frac{1}{99.100}\right)=100x\)
\(\Rightarrow99x+\left(1-\frac{1}{100}\right)=100x\)
\(\Rightarrow99x+\frac{99}{100}=100x\)
\(\Rightarrow x=\frac{99}{100}\left(TMĐK:x\ge0\right)\)
