\(\frac{1}{15}+\frac{1}{21}+...+\frac{2}{x.\left(x+1\right)}=\frac{806}{2015}\)
\(\Rightarrow2.\left(\frac{1}{30}+\frac{1}{42}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{806}{2015}\)
\(\Rightarrow2.\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{806}{2015}\)
\(\Rightarrow2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{806}{2015}\)
\(\Rightarrow2.\left(\frac{1}{5}-\frac{1}{x}\right)=\frac{806}{2015}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x}=\frac{806}{2015}:2\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{x}=\frac{1}{5}-\frac{403}{2015}\)
\(\Rightarrow\frac{1}{x}=\frac{403}{2015}-\frac{403}{2015}\)
\(\Rightarrow\frac{1}{x}=0\)
\(\Rightarrow x=0\)
Vậy \(x=0\)
Chúc bạn học tốt !!!!
\(\Rightarrow\frac{1}{2}\left(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{2}{x\left(x+1\right)}\right)=\frac{806}{2015}.\frac{1}{2}\)
\(\Rightarrow\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{x\left(x+1\right)}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+1\right)}=\frac{403}{2015}\)
\(\Rightarrow\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+...+\frac{x+1-x}{x\left(x+1\right)}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{5}-\frac{1}{x+1}=\frac{403}{2015}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{5}-\frac{403}{2015}\)
rồi bạn tự giải nốt nhé