Giải thích các bước giải:
$+) A=\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}...+\dfrac{1}{70}\\
=\left ( \dfrac{1}{11}+\dfrac{1}{12}+...+\dfrac{1}{30} \right )+\left ( \dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{50} \right )+\left ( \dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{70} \right )\\
>\dfrac{1}{30}.20+\dfrac{1}{50}.20+\dfrac{1}{70}.20\\
=\dfrac{2}{3}+\dfrac{2}{5}+\dfrac{2}{7}\\
=\dfrac{2.35}{105}+\dfrac{2.21}{105}+\dfrac{2.15}{105}\\
=\dfrac{142}{105}\\
>\dfrac{140}{105}\\
=\dfrac{4}{3}\\
+) A=\dfrac{1}{11}+\dfrac{1}{12}+\dfrac{1}{13}...+\dfrac{1}{70}\\
=\left ( \dfrac{1}{11}+\dfrac{1}{12}+...+\dfrac{1}{30} \right )+\left ( \dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{50} \right )+\left ( \dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{70} \right )\\
=\left ( \dfrac{1}{11}+...+\dfrac{1}{20} \right )+\left ( \dfrac{1}{21}+...+\dfrac{1}{30} \right )+\left ( \dfrac{1}{31}+...+\dfrac{1}{40} \right )+\left ( \dfrac{1}{41}+...+\dfrac{1}{50} \right )+\left ( \dfrac{1}{51}+...+\dfrac{1}{60} \right )+\left ( \dfrac{1}{61}+...+\dfrac{1}{70} \right )\\
<\dfrac{1}{11}.10+\dfrac{1}{21}.10+\dfrac{1}{31}.10+\dfrac{1}{41}.10+\dfrac{1}{51}.10+\dfrac{1}{61}.10\\
<1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}\\
=1+\left ( \dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6} \right )+\left ( \dfrac{1}{4}+\dfrac{1}{5} \right )\\
<2+0,5\\
=2,5$
