Ta có: \(\frac{1}{1\cdot3}-\frac{2}{3\cdot5}+\frac{3}{5\cdot7}-\frac{4}{7\cdot9}+\frac{5}{9\cdot11}\)
\(=\frac14\left(\frac{4}{1\cdot3}-\frac{8}{3\cdot5}+\frac{12}{5\cdot7}-\frac{16}{7\cdot9}+\frac{20}{9\cdot11}\right)\)
\(=\frac14\left(1+\frac13-\frac13-\frac15+\frac15+\frac17-\frac17-\frac19+\frac19+\frac{1}{11}\right)\)
\(=\frac14\left(1+\frac{1}{11}\right)=\frac14\cdot\frac{12}{11}=\frac{3}{11}\)
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