a, (2/3-1-4+5/11):(5/12-1-7/11) b,2.x mũ 2 -72=0 c, Rút gọn A=1+1/2+1/2^2+1/3^3+…+1/2^2020

0 bình luận về “a, (2/3-1-4+5/11):(5/12-1-7/11) b,2.x mũ 2 -72=0 c, Rút gọn A=1+1/2+1/2^2+1/3^3+…+1/2^2020”

1. Đáp án:

    $a)\dfrac{512}{161}\\
   b)
   x=\pm 6\\
   c)A=2-\dfrac{1}{2^{2020}}$

   Giải thích các bước giải:

    $a)\left ( \dfrac{2}{3}-1-4+\dfrac{5}{11} \right ):\left ( \dfrac{5}{12}-1-\dfrac{7}{11} \right )\\
   =\left ( \dfrac{2.11}{33}-\dfrac{5.33}{33}+\dfrac{15}{33} \right ):\left ( \dfrac{5.11}{12.11}-\dfrac{11.12}{11.12}-\dfrac{7.12}{12.11} \right )\\
   =\dfrac{-128}{3.11}:\dfrac{-161}{11.12}\\
   =\dfrac{128}{3.11}.\dfrac{11.12}{161}\\
   =\dfrac{128.4}{161}\\
   =\dfrac{512}{161}\\
   b)
   2.x^2-72=0\\
   \Leftrightarrow 2.x^2=72\\
   \Leftrightarrow x^2=36\\
   \Leftrightarrow x=\pm \sqrt{36}=\pm 6\\
   c)A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+…+\dfrac{1}{2^{2020}}\\
   \Rightarrow 2A=2+1+\dfrac{1}{2}+\dfrac{1}{2^2}+…+\dfrac{1}{2^{2019}}\\
   A=2A-A=2+1+\dfrac{1}{2}+\dfrac{1}{2^2}+…+\dfrac{1}{2^{2019}}-\left ( 1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+…+\dfrac{1}{2^{2020}} \right )\\
   =2+1+\dfrac{1}{2}+\dfrac{1}{2^2}+…+\dfrac{1}{2^{2019}}- 1-\dfrac{1}{2}-\dfrac{1}{2^2}-\dfrac{1}{2^3}-…-\dfrac{1}{2^{2020}} \\
   =2-\dfrac{1}{2^{2020}}$

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