Thực hiện các phép tính sau bằng cách hợp lí:
\(A=\dfrac{\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+...+\dfrac{1}{50}\right)\cdot\left(1+2+3+...+50\right)\cdot\left(48\cdot1,5-1,2\cdot60\right)}{2+4+6+...+50}\)
\(B=\dfrac{\dfrac{1}{5}+\dfrac{1}{12}-\dfrac{1}{13}}{\dfrac{7}{5}+\dfrac{7}{12}-\dfrac{7}{13}}-\dfrac{\dfrac{2}{3}-\dfrac{2}{9}-\dfrac{2}{15}+\dfrac{2}{21}}{\dfrac{7}{3}-\dfrac{7}{9}-\dfrac{7}{15}+\dfrac{1}{3}}\)
\(B=\dfrac{\dfrac{1}{5}+\dfrac{1}{12}-\dfrac{1}{13}}{\dfrac{7}{5}+\dfrac{7}{12}-\dfrac{7}{13}}-\dfrac{\dfrac{2}{3}-\dfrac{2}{9}-\dfrac{2}{15}+\dfrac{2}{21}}{\dfrac{7}{3}-\dfrac{7}{9}-\dfrac{7}{15}+\dfrac{1}{3}}\)
\(B=\dfrac{\dfrac{1}{5}+\dfrac{1}{12}-\dfrac{1}{13}}{7.\left(\dfrac{1}{5}+\dfrac{1}{12}-\dfrac{1}{13}\right)}-\dfrac{2.\left(\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{15}+\dfrac{1}{21}\right)}{\dfrac{7}{3}-\dfrac{7}{9}-\dfrac{7}{15}+\dfrac{7}{21}}\)
\(B=\dfrac{1}{7}-\dfrac{2.\left(\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{15}+\dfrac{1}{21}\right)}{7.\left(\dfrac{1}{3}-\dfrac{1}{9}-\dfrac{1}{15}+\dfrac{1}{21}\right)}\)
\(B=\dfrac{1}{7}-\dfrac{2}{7}\)
\(B=\dfrac{-1}{7}\)
\(...A=\dfrac{\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{50}\right)\left(1+2+3+...+25\right)\left(72-72\right)}{2\left(1+2+3+...+25\right)}=0\)
