\(2\times x-\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}=\frac{3}{11}\)
\(2\times x-2\times\frac{1}{12}+\left(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)=\frac{3}{11}\)
\(2\times\left(x-\frac{1}{12}\right)+\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)=\frac{3}{11}\)
\(2\times\left(x-\frac{1}{12}\right)+\left(\frac{1}{3}-\frac{1}{10}\right)=\frac{3}{11}\)
\(2\times\left(x-\frac{1}{12}\right)+\frac{7}{30}=\frac{3}{11}\)
\(2\times\left(x-\frac{1}{12}\right)=\frac{13}{330}\)
\(x-\frac{1}{12}=\frac{13}{660}\)
\(x=\frac{17}{165}\)
\(2x-\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}=\frac{3}{11}\)
\(\Rightarrow2x-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)=\frac{3}{11}\)
\(\Rightarrow2x-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)=\frac{3}{11}\)
\(\Rightarrow2x-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)=\frac{3}{11}\)
\(\Rightarrow2x-\left(\frac{1}{2}-\frac{1}{10}\right)=\frac{3}{11}\)
\(\Rightarrow2x-\frac{2}{5}=\frac{3}{11}\)
\(\Rightarrow2x=\frac{3}{11}+\frac{2}{5}\)
\(\Rightarrow2x=\frac{37}{55}\)
\(\Rightarrow x=\frac{37}{55}:2\)
\(\Rightarrow x=\frac{37}{110}\)
Vậy \(x=\frac{37}{110}\)
_Chúc bạn học tốt_
