Đáp án:
$A=\dfrac{2900}{63}$
Giải thích các bước giải:
$A=\dfrac{\dfrac{5^3}{6}+\dfrac{5^3}{12}+\dfrac{5^3}{20}+\dfrac{5^3}{30}+\dfrac{5^3}{42}+\dfrac{5^3}{90}}{\dfrac{24.47-23}{24+23.47}}\\
=\dfrac{5^3.\left (\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{9.10} \right )}{\dfrac{(23+1).47-23}{24+23.47}}\\
=\dfrac{5^3.\left (\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{90} \right )}{\dfrac{23.47+47-23}{24+23.47}}\\
=\dfrac{5^3.\left (\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{90} \right )}{\dfrac{23.47+24}{24+23.47}}\\
=\dfrac{5^3.\left (\dfrac{315}{630}-\dfrac{90}{630}+\dfrac{7}{630} \right )}{1}\\
=5^3.\dfrac{315-90+7}{630}\\
=5^3.\dfrac{232}{630}\\
=5^3\dfrac{116}{315}\\
=\dfrac{125.116}{315}\\
=\dfrac{2900}{63}$
