A= 5.(1/5.6+1/6.7+...+1/10.11)
A=5.(1/5-1/6+1/6-1/7+.....+1/10-1/11)
A=5.(1/5-1/11)
A=5.6/55=6/11
Ta có: \(A=\frac{5}{5x6}+\frac{5}{6x7}+\frac{5}{7x8}+\frac{5}{8x9}+\frac{5}{9x10}+\frac{5}{10x11}.\)
\(=5\left(\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{7x8}+...+\frac{1}{10x11}\right)\)
\(=5\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(=5\left(\frac{1}{5}-\frac{1}{11}\right)=5x\frac{6}{55}=\frac{6}{11}\)