\(S=\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{59.61}\)
\(S=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.60}\right)\)
\(S=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{60}\right)\)
\(S=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{60}\right)\)
\(S=\frac{3}{2}.\left(\frac{12}{60}-\frac{1}{60}\right)\)
\(S=\frac{3}{2}.\frac{11}{60}\)
\(S=\frac{11}{40}\)
\(S=\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+...+\frac{3}{59\cdot61}\)
\(S=\frac{3}{2}\left[\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{59\cdot61}\right]\)
\(S=\frac{3}{2}\left[\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{59}-\frac{1}{61}\right]\)
\(S=\frac{3}{2}\left[\frac{1}{5}-\frac{1}{61}\right]=\frac{3}{2}\cdot\frac{56}{305}=\frac{84}{305}\)
\(\Rightarrow S=3\left(\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{59.61}\right)\)
Đặt \(A=\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{59.61}\)=> \(2A=\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{59.61}\)
=> \(2A=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\)
=> \(2A=\frac{1}{5}-\frac{1}{61}\Rightarrow A=\frac{28}{305}\)
=> \(S=3.\frac{28}{305}=\frac{84}{305}\)Vậy \(S=\frac{84}{305}\)
Chúc bn hok tốt...Nếu đúng k cho mik nha
