Question

4/5x7+4/7x9+4/9x11+4/11*13.........+4/99x101

/ là dấu gạch ngang giữa phân số

Answer 1

\(\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+...+\frac{4}{99.101}\)

\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{99.101}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{101}\right)\)

\(=2.\frac{96}{505}\)

\(=\frac{192}{505}\)