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