A=$\frac{1}{11}$+$\frac{1}{12}$+$\frac{1}{13}$+….+$\frac{1}{70}$ Chứng minh $\frac{4}{3}$

09/10/2021 Bởi aikhanh

0 bình luận về “A=$\frac{1}{11}$+$\frac{1}{12}$+$\frac{1}{13}$+….+$\frac{1}{70}$ Chứng minh $\frac{4}{3}$<A<2,5”

1. Giải thích các bước giải:

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

   Bình luận