Bài 1

1)\(\dfrac{1}{2011}.x+\left(\dfrac{1}{2}+\dfrac{1}{6}+....+\dfrac{1}{2010.2011}\right)=1\)

\(\dfrac{1}{2011}.x+\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+....+\dfrac{1}{2010.2011}\right)=1\)

\(\dfrac{1}{2011}.x+\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2010}-\dfrac{1}{2011}\right)=1\)

\(\dfrac{1}{2011}.x+\left(1-\dfrac{1}{2011}\right)=1\)

\(\dfrac{1}{2011}.x+\left(\dfrac{2010}{2011}-\dfrac{1}{2011}\right)=1\)

\(\dfrac{1}{2011}.x+\dfrac{2010}{2011}=1\)

\(\dfrac{1}{2011}.x=1-\dfrac{2010}{2011}\)

\(\dfrac{1}{2011}.x=\dfrac{1}{2011}\)

\(x=\dfrac{1}{2011}\div\dfrac{1}{2011}\)

\(x=1\)

\(Vậyx=1\)