\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\\ \Rightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\\ \Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\\ 2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2013}{2015}\\ \Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{2015}:2\\ \Rightarrow-\frac{1}{x+1}=\frac{2013}{4030}-\frac{1}{2}\\ \Rightarrow-\frac{1}{x+1}=-\frac{1}{2015}\\ \Rightarrow x=2015\)
Vậy x=2015
\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\\ \Rightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\\ \Rightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\\ 2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2013}{2015}\\ \Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2013}{2015}:2\\ \Rightarrow-\frac{1}{x+1}=\frac{2013}{4030}\\ \Rightarrow-\frac{1}{x+1}=-\frac{1}{2015}\\ \Rightarrow x+1=2015\\ \Rightarrow x=2014\)
Vậy x=2014
xin lỗi nhé! vừa nãy mình vội quá nên làm nhầm
