\(\left(x-10\right)\cdot\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{200}}{\dfrac{1}{199}+\dfrac{2}{198}+...+\dfrac{199}{1}}=\dfrac{1}{200}\)
=>\(\left(x-10\right)\cdot\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{200}}{\left(1+\dfrac{1}{199}\right)+\left(1+\dfrac{2}{198}\right)+...+\left(1+\dfrac{1}{2}\right)+1}=200\)
=>\(\left(x-10\right)\cdot\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{200}}{\dfrac{200}{199}+\dfrac{200}{198}+...+\dfrac{200}{2}+\dfrac{200}{200}}=\dfrac{1}{200}\)
=>\(\left(x-10\right)\cdot\dfrac{1}{200}=\dfrac{1}{200}\)
=>x-10=1
=>x=11