\(C=\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}=\frac{5}{5}\cdot\left(\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}\right)\)
\(=\frac{1}{5}\cdot\left(\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+...+\frac{5}{61\cdot66}\right)=\frac{1}{5}\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\cdot\left[\left(\frac{1}{11}-\frac{1}{66}\right)+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)\right]\)
\(=\frac{1}{5}\cdot\left[\left(\frac{6}{66}-\frac{1}{66}\right)+0+...+0\right]=\frac{1}{5}\cdot\frac{5}{66}=\frac{1\cdot5}{5\cdot66}=\frac{1\cdot1}{1\cdot66}=\frac{1}{66}\)
Vậy \(C=\frac{1}{66}\)
Chúc bạn học tốt!^_^
