Ta có: \(x+2x+3x+4x+...+100x+50=5200\)
\(\Leftrightarrow x\left(1+2+3+4+...+100\right)=5150\)
\(\Leftrightarrow x\cdot\frac{\left(1+100\right)\cdot\left[\left(100-1\right)\div1+1\right]}{2}=5150\)
\(\Leftrightarrow x\cdot5050=5150\)
\(\Rightarrow x=\frac{103}{101}\)