Đáp án:
$A=\dfrac{27}{4}+\dfrac{72}{9}+\dfrac{135}{16}+\dfrac{216}{25}+..+\dfrac{891}{100}$
$⇒ A=9\bigg(\dfrac{3}{4}+\dfrac{8}{9}+\dfrac{15}{16}+\dfrac{24}{25}+..+\dfrac{99}{100}\bigg)$
\[⇒ A=9\bigg(1-\dfrac{1}{2^2}+1-\dfrac{1}{3^2}+1-\dfrac{1}{4^2}+1-\dfrac{1}{5^2}+..+1-\dfrac{1}{10^2}\bigg)\] \[⇒A=9\bigg(9-\dfrac{1}{2^2}-\dfrac{1}{3^2}+...-\dfrac{1}{10^2}\bigg)\] \[⇒A>9\bigg[9-\bigg(\dfrac{1}{1.2}+\dfrac{1}{2.3}+....+\dfrac{1}{9.10}\bigg)\bigg]\] \[⇒A>9\bigg[9-\bigg(1-\dfrac{1}{10}\bigg)\bigg]=\dfrac{729}{10}>\dfrac{480}{7}\]
\[B=\dfrac{144}{3}+\dfrac{144}{15}+\dfrac{144}{35}+..+\dfrac{144}{399}\]
$⇒ B=72(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+..+\dfrac{2}{19.21})$
$⇒ B=72(\dfrac11-\dfrac13+\dfrac13-\dfrac15+\dfrac15-\dfrac17+..+\dfrac{1}{19}-\dfrac{1}{21})$
$⇒ B=72(1-\dfrac{1}{21})=\dfrac{480}{7}$
\[⇒A>B\]
