Bài 1:Tính: a,A=1/3-(+3/4)-(+3/5)++1/57-1/36+1/15-2/9 b,B=1/2.1/4+1/2.1/5+1/2.1/-4 Bài 2:Tính: a,A=7/1.3+7/3.5+7/5.7+7/7.9+…+7/19.21 b,B=1/2+1/6=1/2

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1. Đáp án:

    $1)
   a)
   A=\dfrac{-337}{285}\\
   b)
   B=\dfrac{1}{10}\\
   2)
   a)
   A=\dfrac{10}{3}\\
   b)
   B=\dfrac{71}{120}$

   Giải thích các bước giải:

    $1)
   a)
   A=\dfrac{1}{3}-\left ( \dfrac{3}{4} \right )-\left ( \dfrac{3}{5} \right )+\dfrac{1}{57}-\dfrac{1}{36}+\dfrac{1}{15}-\dfrac{2}{9}\\
   =\left (\dfrac{1}{3}-\dfrac{2}{9}  \right )\left(-\dfrac{3}{4}-\dfrac{1}{36}\right)+\left ( -\dfrac{3}{5} +\dfrac{1}{15}  \right )+\dfrac{1}{57}\\
   =\left (\dfrac{3}{9}-\dfrac{2}{9}  \right )+\left(-\dfrac{27}{36}-\dfrac{1}{36}\right)+\left ( -\dfrac{9}{15} +\dfrac{1}{15}  \right )+\dfrac{1}{57}\\
   =\dfrac{1}{9}-\dfrac{28}{36}-\dfrac{8}{15}+\dfrac{1}{57}\\
   =\dfrac{4}{36}-\dfrac{28}{36}-\dfrac{8}{15}+\dfrac{1}{57}\\
   =\dfrac{-24}{36}-\dfrac{8}{15}+\dfrac{1}{57}\\
   =\dfrac{-2}{3}-\dfrac{8}{15}+\dfrac{1}{57}\\
   =\dfrac{-10}{15}-\dfrac{8}{15}+\dfrac{1}{57}\\
   =\dfrac{-18}{15}+\dfrac{1}{57}\\
   =\dfrac{(-18).19}{285}+\dfrac{5}{285}\\
   =\dfrac{-337}{285}\\
   b)
   B=\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{2}.\dfrac{1}{5}+\dfrac{1}{2}.\dfrac{1}{-4}\\
   =\dfrac{1}{2}.\dfrac{1}{4}-\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{2}.\dfrac{1}{5}\\
   =\dfrac{1}{10}\\
   2)
   a)
   A=\dfrac{7}{1.3}+\dfrac{7}{3.5}+\dfrac{7}{5.7}+\dfrac{7}{7.9}+…+\dfrac{7}{19.21}\\
   =\dfrac{7}{2}.\left ( \dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+…+\dfrac{2}{19.21} \right )\\
   =\dfrac{7}{2}.\left ( 1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+…+\dfrac{1}{19}-\dfrac{1}{21} \right )\\
   =\dfrac{7}{2}.\left ( 1-\dfrac{1}{21} \right )\\
   =\dfrac{7}{2}.\left ( \dfrac{21}{21}-\dfrac{1}{21} \right )\\
   =\dfrac{7}{2}.\dfrac{20}{21}\\
   =\dfrac{10}{3}\\
   b)
   B=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{-5}\\
   =\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{-5}\\
   =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}-\dfrac{1}{5}\\
   =1-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{8}-\dfrac{1}{5}\\
   =\dfrac{120}{120}-\dfrac{40}{120}+\dfrac{30}{120}-\dfrac{15}{120}-\dfrac{24}{120}\\
   =\dfrac{71}{120}$

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