Question

6/35+6/63+6/99+...+6/255=...                

tính nhanh

Answer 1

\(\frac{6}{35}+\frac{6}{63}+\frac{6}{99}+...+\frac{6}{255}\)

\(=3\left(\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+...+\frac{2}{255}\right)\)

\(=3\left(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+...+\frac{2}{15\cdot17}\right)\)

\(=3\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{15}-\frac{1}{17}\right)\)

\(=3\left(\frac{1}{5}-\frac{1}{17}\right)\)

\(=3\cdot\frac{12}{85}=\frac{36}{85}\)

Answer 2

thanks