\(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{\left(3x-2\right)\left(3x+1\right)}=\frac{670}{2011}\)
\(\Rightarrow\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{\left(3x-2\right)\left(3x+1\right)}\right)=\frac{670}{2011}\)
\(\Rightarrow1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{3x-2}-\frac{1}{3x+1}=\frac{670}{2011}:\frac{1}{3}\)
\(\Rightarrow1-\frac{1}{3x+1}=\frac{2010}{2011}\)
\(\Rightarrow\frac{1}{3x+1}=1-\frac{2010}{2011}\)
\(\Rightarrow\frac{1}{3x+1}=\frac{1}{2011}\)
=>3x+1=2011
=>3x=2011-1
=>x=2010:3
=>x=670
vậy x=670
Dặt \(A=\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{\left(3x-2\right).\left(3x+1\right)}\)
\(3A=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{\left(3x-2\right)\left(3x+1\right)}\)
\(3A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{\left(3x-2\right)}-\frac{1}{\left(3x+1\right)}\)
\(3A=1-\frac{1}{3x+1}\)
\(A=\left(1-\frac{1}{3x+1}\right):3=\frac{670}{2011}\)
\(1-\frac{1}{3x+1}=\frac{670}{2011}.3\)
\(1-\frac{1}{3x+1}=\frac{2010}{2011}\)
\(\frac{1}{3x+1}=1-\frac{2010}{2011}\)suy ra \(\frac{1}{3x+1}=\frac{1}{2011}\)
suy ra 3x+1=2011
3x=2000
x=2000/3
