Ta có: \(A=\frac{4}{1\times3}+\frac{12}{5\times7}+\frac{20}{9\times11}+\frac{28}{13\times15}\)
\(=1+\frac13+\frac15+\frac17+\frac19+\frac{1}{11}+\frac{1}{13}+\frac{1}{15}\)
Ta có: \(B=\frac{8}{3\times5}+\frac{16}{7\times9}+\frac{24}{11\times13}+\frac{32}{15\times17}\)
\(=\frac13+\frac15+\frac17+\frac19+\frac{1}{11}+\frac{1}{13}+\frac{1}{15}+\frac{1}{17}\)
Do đó: A-B=\(=1+\frac13+\frac15+\frac17+\frac19+\frac{1}{11}+\frac{1}{13}+\frac{1}{15}-\left(\frac13+\frac15+\frac17+\frac19+\frac{1}{11}+\frac{1}{13}+\frac{1}{15}+\frac{1}{17}\right)\)
\(=1+\frac13+\frac15+\frac17+\frac19+\frac{1}{11}+\frac{1}{13}+\frac{1}{15}-\frac13-\frac15-\frac17-\frac19-\frac{1}{11}-\frac{1}{13}-\frac{1}{15}-\frac{1}{17}\)
\(=1-\frac{1}{17}=\frac{16}{17}\)
4 và 5
