P=2^50+2^49+2^48+…+2^2+2+1. So sánh P& 2^51

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1. Đáp án:

   P=2^50+2^49+2^48+…+2^2+2+1 >P= 2^51

   Giải thích các bước giải:

   P=2^50+2^49+2^48+…+2^2+2+1

   P2=2^51+2^50+2^49+…+2^3+2^2+2

   P2-P=(2^51+2^50+2^49+…+2^3+2^2+2)-(2^50+2^49+2^48+…+2^2+2+1)

   P=2^51+2-1

   P=2^51+3>P=2^51

   ⇒P=2^50+2^49+2^48+…+2^2+2+1 >P= 2^51

   #Nocopy

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2. Đáp án: $P < 2^{51}$.

   Giải thích các bước giải:

   $P = 2^{50} + 2^{49} + 2^{48} + … + 2^2 + 2^1$

   $⇔ 2P = 2^{51} + 2^{50} + 2^{49} + … + 2^3 + 2^2$

   $⇔ 2P – P = (2^{51} + 2^{50} + 2^{49} + … + 2^3 + 2^2)-(2^{50} + 2^{49} + 2^{48} + … + 2^2 + 2^1)$

   $⇔ P = 2^{51} – 2$

   $⇒$ $P = 2^{51} – 2 < 2^{51}$.

    

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