a/ 3/2.4 + 3/6.8 +…..+ 3/98 .100 b/ 6 /15.16 +6 / 18.21 +6 /21.24 +….. + 6/ 72.75

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1. Đáp án:

    $a)
   \dfrac{147}{200}\\
   b)\dfrac{8}{75}$

   Giải thích các bước giải:

   $a)
   \dfrac{3}{2.4}+\dfrac{3}{4.6}+\dfrac{3}{6.8}+…+\dfrac{3}{98.100}\\
   =\dfrac{3}{2}.\left ( \dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+…+\dfrac{2}{98.100} \right )\\
   =\dfrac{3}{2}.\left ( \dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+…+\dfrac{1}{98}-\dfrac{1}{100} \right )\\
   =\dfrac{3}{2}.\left ( \dfrac{1}{2}-\dfrac{1}{100} \right )\\
   =\dfrac{3}{2}.\left ( \dfrac{50}{100}-\dfrac{1}{100} \right )\\
   =\dfrac{3}{2}.\dfrac{49}{100}=\dfrac{147}{200}\\
   b)\dfrac{6}{15.18}+\dfrac{6}{18.21}+\dfrac{6}{21.24}+…+\dfrac{6}{72.75}\\
   =2.\left ( \dfrac{3}{15.18}+\dfrac{3}{16.18}+\dfrac{3}{18.21}+\dfrac{3}{21.24}+…+\dfrac{3}{72.75} \right )\\
   =2.\left ( \dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+…+\dfrac{1}{72}-\dfrac{1}{75} \right )\\
   =2.\left ( \dfrac{1}{15}-\dfrac{1}{75} \right )\\
   =2.\left ( \dfrac{5}{75}-\dfrac{1}{75} \right )\\
   =2.\dfrac{4}{75}=\dfrac{8}{75}$ 

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