Question

[Bùi Phương Thảo]

4/9,11+4/11,13+.....+4/109,111

Answer 1

[Đoàn Đức Hà]

\(\frac{4}{9\times11}+\frac{4}{11\times13}+...+\frac{4}{109\times111}\)

\(=2\times\left(\frac{2}{9\times11}+\frac{2}{11\times13}+...+\frac{2}{109\times111}\right)\)

\(=2\times\left(\frac{11-9}{9\times11}+\frac{13-11}{11\times13}+...+\frac{111-109}{109\times111}\right)\)

\(=2\times\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+...+\frac{1}{109}-\frac{1}{111}\right)\)

\(=2\times\left(\frac{1}{9}-\frac{1}{111}\right)\)

\(=\frac{68}{333}\)