Ta có:
\(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{97.99}\)
\(=\frac{2}{11}-\frac{2}{13}+\frac{2}{13}-\frac{2}{15}+\frac{2}{15}-\frac{2}{17}+...+\frac{2}{97}-\frac{2}{99}\)
\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{1}{11}-\frac{1}{99}=\frac{8}{99}\)
Sửa lại đề bài nhé:
\(\frac{2}{11x13}+\frac{2}{13x15}+\frac{2}{15x17}+.........+\frac{2}{97x99}\)
= \(\frac{2}{11}-\frac{2}{13}+\frac{2}{13}-\frac{2}{15}+\frac{2}{15}-\frac{2}{17}+..........+\frac{2}{97}-\frac{2}{99}\)
Sau khi trực tiêu hết ta có:
= \(\frac{2}{11}-\frac{2}{99}\)
= \(\frac{16}{19}\)
\(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+....+\frac{2}{97.99}\)
\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{1}{11}-\frac{1}{99}=\frac{9}{99}-\frac{1}{99}=\frac{8}{99}\)
Sửa đề :
\(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{97.99}\)
\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}\)
\(=\frac{8}{99}\)
