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toán 1 sao?
\(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+...+\frac{5}{53\cdot55}\)
\(=\frac{3}{2}\cdot\left(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{53\cdot55}\right)\)
\(=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{53}-\frac{1}{55}\right)\)
\(=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{55}\right)\)
\(=\frac{3}{2}\cdot\left(\frac{11}{55}-\frac{1}{55}\right)\)
\(=\frac{3}{2}\cdot\frac{10}{55}\)
\(=\frac{3}{2}\cdot\frac{2}{11}\)
\(=\frac{3}{11}\)