Đáp án:
$5)
a)C=\dfrac{1}{9}\\
b)
D=\dfrac{1}{325}$
Giải thích các bước giải:
$5)
a)C=\dfrac{6}{15.18}+\dfrac{6}{18.21}+\dfrac{6}{21.24}+...+\dfrac{6}{87.90}\\
=2.\left (\dfrac{3}{15.18}+\dfrac{3}{18.21}+\dfrac{3}{21.24}+...+\dfrac{3}{87.90} \right )\\
=2.\left ( \dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{87}-\dfrac{1}{90} \right )\\
=2.\left ( \dfrac{1}{15}-\dfrac{1}{90} \right )\\
=2.\left ( \dfrac{6}{90}-\dfrac{1}{90} \right )\\
=2.\dfrac{5}{90}\\
=\dfrac{1}{9}\\
b)
D=\left [ \left ( 1-\dfrac{1}{2} \right ).\left ( 1-\dfrac{1}{3} \right ).\left ( 1-\dfrac{1}{4} \right )...\left ( 1-\dfrac{1}{25} \right ) \right ]:\left [ \left ( 1+\dfrac{1}{2} \right ).\left ( 1+\dfrac{1}{3} \right )\left ( 1+\dfrac{1}{4} \right )...\left ( 1+\dfrac{1}{25} \right ) \right ]\\
=\left [\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{24}{25} \right ]:\left [ \dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{26}{25} \right ]\\
=\dfrac{1}{25}:\dfrac{26}{2}\\
=\dfrac{1}{25}:13\\
=\dfrac{1}{25}.\dfrac{1}{13}\\
=\dfrac{1}{325}$
