Question

tìm x biết; /x+1:(1.5)/+ /x+1: (5.9)/+........+ /x +1: (397.401)/=101x

Answer 1

Ta có: \(|x+\frac{1}{1\cdot5}|+|x+\frac{1}{5\cdot9}|+...+|x+\frac{1}{397\cdot401}|=101x\ge0\)

\(\Rightarrow x\ge0\Rightarrow x+\frac{1}{1\cdot5}+x+\frac{1}{5\cdot9}+...+x+\frac{1}{397\cdot401}=101x\)

\(\Rightarrow100x+\frac{1}{4}\cdot\left(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+...+\frac{4}{397\cdot401}\right)=101x\)

\(\Rightarrow\frac{1}{4}\cdot\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{397}-\frac{1}{401}\right)=101x-100x=x\)

\(\Rightarrow\frac{1}{4}\cdot\frac{400}{401}=\frac{100}{401}=x\)