Question

G=\(\frac{7}{1\cdot5}\)+\(\frac{7}{5\cdot9}\)+\(\frac{7}{9\cdot13}\)+\(\frac{7}{13\cdot17}\)+\(\frac{7}{17\cdot21}\)+\(\frac{7}{21\cdot23}\)                                                                                               

H=\(\frac{1}{2}\)+\(\frac{1}{6}\)+\(\frac{1}{12}\)+\(\frac{1}{20}\)+\(\frac{1}{30}\)+\(\frac{1}{42}\)+...............+\(\frac{1}{110}\)                                                                                                  

Answer 1

Mình sửa lại đề bạn sai nhé\(G=\frac{7}{1.5}+\frac{7}{5.9}+\frac{7}{9.13}+....+\frac{7}{21.25}\)

   \(=\frac{7.4}{1.5.4}+\frac{7.4}{5.9.4}+\frac{7.4}{9.13.4}+....+\frac{7.4}{21.25.4}\)

    \(=\frac{7}{4}.\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+....+\frac{4}{21.25}\right)\)

    \(=\frac{7}{4}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{21}-\frac{1}{25}\right)\)

   \(=\frac{7}{4}.\left(1-\frac{1}{25}\right)\)

    \(=\frac{7}{4}.\frac{24}{25}\)

   \(\frac{42}{25}\)