c) Chứng minh B = 1 + 1/2 +1/3 + ….+ 1/2^2021 -1 < 2021 trl đúng toi cho 5 sao + trl hay nhất + cảm ơn

1 bình luận về “c) Chứng minh B = 1 + 1/2 +1/3 + ….+ 1/2^2021 -1 < 2021 trl đúng toi cho 5 sao + trl hay nhất + cảm ơn”

1. c,

   B = 1 + 1/2 + … + 1/(2^2021 – 1)

   = 1 + (1/2 + 1/3) + (1/4 + 1/5 + 1/6 + 1/7) + … + (1/2^(n – 1) + … + 1/(2^n – 1))

   = 1 + (1/2^(2 – 1) + 1/(2^2 – 1)) + (1/2^(3 – 1) + … + 1/(2^3 – 1)) + … + (1/2^(n – 1) + … + 1/(2^n – 1))

   Vì: 1/2^(n – 1) = 1/2^(n – 1)

   1/(2^(n – 1) + 1) < 1/2^(n – 1)

   1/(2^(n – 1) + 2) < 1/2^(n – 1)

   …

   1/(2^n – 1) < 1/2^(n – 1)

   => 1/2^(n – 1) + … + 1/(2^n – 1) < 2^(n – 1) . 1/2^(n – 1)

   => B < 1 + 2 . 1/2 + 4. 1/4 + … + 2^(n – 1) . 1/2^(n – 1)

   < 1 + 1 + … + 1 = 2021

   Vậy B < 2021.

    

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