Các bạn giúp mk với. Mk cần gấp
\(\frac{-3}{15}+\frac{-3}{35}+\frac{-3}{63}+\frac{-3}{99}+\frac{-3}{143}+\frac{-3}{195}\)
\(=\frac{-3}{3.5}+\frac{-3}{5.7}+\frac{-3}{7.9}+\frac{-3}{9.11}+\frac{-3}{11.13}+\frac{-3}{13.15}\)
\(=\frac{-3}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.25}\right)\)
\(=\frac{-3}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{-3}{2}.\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{-3}{2}.\frac{4}{15}=\frac{-2}{5}\)
\(=\frac{-3}{3\cdot5}+\frac{-3}{5\cdot7}+\frac{-3}{7\cdot9}+...+\frac{-3}{13\cdot15}\)
\(=-\frac{3}{2}\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{13\cdot15}\right)\)
\(=-\frac{3}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{13}-\frac{1}{15}\right)\)
\(=-\frac{3}{2}\left(\frac{1}{3}-\frac{1}{15}\right)\)
\(=-\frac{3}{2}\cdot\frac{4}{15}\)
\(=\frac{-2}{5}\)
