\(A=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{49.51}\)
\(A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{49}-\dfrac{1}{51}\)
\(A=1-\dfrac{1}{51}=\dfrac{50}{51}\)
Câu B làm tương tự câu A
b) \(B=\dfrac{3}{1.5}+\dfrac{3}{5.9}+\dfrac{3}{9.13}+\dfrac{3}{13+17}+\dfrac{3}{17+21}+\dfrac{3}{21.25}+\dfrac{3}{25.29}\)\(B=3.\left(\dfrac{1}{1.5}+\dfrac{1}{5.9}+\dfrac{1}{9.13}+\dfrac{1}{13+17}+\dfrac{1}{17+21}+\dfrac{1}{21.25}+\dfrac{1}{25.29}\right).4:4\)
\(B=\dfrac{3}{4}.\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+\dfrac{4}{9.13}+\dfrac{4}{13+17}+\dfrac{4}{17+21}+\dfrac{4}{21.25}+\dfrac{4}{25.29}\right)\)
\(B=\dfrac{3}{4}.\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+....+\dfrac{1}{25}-\dfrac{1}{29}\right)\)
\(B=\dfrac{3}{4}.\left(1-\dfrac{1}{29}\right)\)
\(B=\dfrac{3}{4}.\dfrac{28}{29}=\dfrac{21}{29}\)
