\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{2}{x\left(x+1\right)}=\frac{2010}{2012}\)
\(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{x\left(x+1\right)}=\frac{2010}{2012}\)
\(\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{x\left(x+1\right)}=\frac{2010}{2012}\)
\(2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2010}{2012}\)
\(2\left(\frac{1}{4}-\frac{1}{x+1}\right)=\frac{2010}{2012}\)
\(\frac{1}{4}-\frac{1}{x+1}=\frac{2010}{2012}\div2\)
\(\frac{1}{4}-\frac{1}{x+1}=\frac{1005}{2012}\)
\(\frac{1}{x+1}=\frac{1}{4}-\frac{1005}{2012}\)
\(\frac{1}{x+1}=\frac{-502}{2012}=-\frac{251}{1006}\)
\(\Rightarrow x+1=1\div-\frac{251}{1006}=-\frac{1006}{251}\)
\(x=\frac{-1006}{251}-1=-\frac{1257}{251}\)
bản rút gọn 2/x(x+1) thanh 1/x(x+1) luon di
