so sánh A = 6 mũ 2019 +1 / 6 mũ 2020 ; B = 6 mũ 2020 +1 / 6 mũ 2021 +1 b) C = 1/2 +1/2 mũ 2 + 1/ 2 mũ 3 +…+1/ 2 mũ 2020 với 1

0 bình luận về “so sánh A = 6 mũ 2019 +1 / 6 mũ 2020 ; B = 6 mũ 2020 +1 / 6 mũ 2021 +1 b) C = 1/2 +1/2 mũ 2 + 1/ 2 mũ 3 +…+1/ 2 mũ 2020 với 1”

1. Giải thích các bước giải:

   a.Ta có:

   $6^{2020}+1<6^{2021}+1$

   $\to \dfrac{6^{2020}+1}{6^{2021}+1}<1$

   $\to \dfrac{6^{2020}+1}{6^{2021}+1}< \dfrac{6^{2020}+1+5}{6^{2021}+1+5}$

   $\to \dfrac{6^{2020}+1}{6^{2021}+1}< \dfrac{6^{2020}+6}{6^{2021}+6}$

   $\to \dfrac{6^{2020}+1}{6^{2021}+1}< \dfrac{6^{2019}+1}{6^{2020}+1}$

   $\to B<A$

   b.Ta có:
   $C=\dfrac12+\dfrac1{2^2}+\dfrac1{2^3}+…+\dfrac1{2^{2020}}$

   $\to 2C=1+\dfrac12+\dfrac1{2^2}+…+\dfrac1{2^{2019}}$

   $\to 2C-C=1-\dfrac1{2^{2020}}$

   $\to C=1-\dfrac1{2^{2020}}$

   $\to C<1$

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