CMR : S=1/2^2-1/2^4+1/2^6-…+1/2^4n-2-1/4n+…+1/2^2002-1/2^2004 <0,2 MN giúp em nhanh nhá :3333

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1. Đáp án:

   $\begin{array}{l}
   S = \dfrac{1}{{{2^2}}} – \dfrac{1}{{{2^4}}} + \dfrac{1}{{{2^6}}} – … + \\
    + \dfrac{1}{{{2^{4n – 2}}}} – \dfrac{1}{{{2^{4n}}}} + … + \dfrac{1}{{{2^{2002}}}} – \dfrac{1}{{{2^{2004}}}}\\
    \Rightarrow {2^2}.S = 1 – \dfrac{1}{{{2^2}}} + \dfrac{1}{{{2^4}}} + … + \dfrac{1}{{{2^{4n}}}} + …\\
    + \dfrac{1}{{{2^{2000}}}} – \dfrac{1}{{{2^{2002}}}}\\
    \Rightarrow 4S + S = 5S = 1 – \dfrac{1}{{{2^{2004}}}}\\
    \Rightarrow S = \dfrac{1}{5} – \dfrac{1}{{{{5.2}^{2004}}}} < \dfrac{1}{5}\\
    \Rightarrow S < 0,2
   \end{array}$

   Vậy S<0,2

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