\((2x-1)+(4x-2)+...+(400x-200)=5+10+...+1000\)
\(\Rightarrow\left(2x+4x+...+400x\right)-\left(1+2+...+200\right)\)
\(=5.\left(1+2+...+200\right)\)
\(\Rightarrow x.\left[\left(400+2\right).200:2\right]-\left[\left(200.\left\{200+1\right\}\right):2\right]\)
\(=5.\left[\left(200.\left\{200+1\right\}\right):2\right]\)
\(\Rightarrow x.40200-20100=100500\)
\(\Rightarrow40200x=120600\)
\(\Rightarrow x=3\)
Vậy \(x=3.\)
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