Question

[Anh chàng lạnh lùng]

Tính nhanh : ( Lưu ý : dấu ( . ) là dấu nhân )

\(A=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.7}+...............+\frac{1}{100.104}\)

Answer 1

[Nguyễn Hưng Phát]

\(A=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+........+\frac{1}{100.104}\)

\(=\frac{1}{4}.\left(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+.......+\frac{4}{100.104}\right)\)

\(=\frac{1}{4}.\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+.......+\frac{1}{100}-\frac{1}{104}\right)\)

\(=\frac{1}{4}.\left(\frac{1}{5}-\frac{1}{104}\right)\)

\(=\frac{1}{4}.\frac{99}{520}=\frac{99}{2080}\)