So sánh A = 2 + 2^2 + … + 2^10 với B = 1/(1 . 2) + 1/(2 . 3) + … + 1/(9 . 10)

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1. `A=2+2^2+2^3+…+2^10`
   

   `2A=2^2+2^3+2^4+…+2^11`
   

   `2A-A=(2^2+2^3+2^4+…+2^11)-(2+2^2+2^3+…+2^10)`
   

   `A=2^11-2`
   

   `A=2048-2=2046`
   

   `B=1/(1 . 2) + 1/(2 . 3) + … + 1/(9 . 10)`
   

   `B=1/1-1/2+1/2-1/3+…+1/9-1/10`
   

   `B=1/1-1/10=10/10-1/10=9/10`
   

   Ta có: `2046=2046/1={2046.10}/{1.10}=20460/10>9/10`
   

   `=>2046>9/10`
   

   `=>A>B`

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2. Đáp án + giải thích bước giải :

   `A = 2 + 2^2 + … + 2^{10}`

   `-> 2A = 2^2 + 2^3 + … + 2^{11}`

   `-> 2A – A = (2^2 + 2^3 + …. + 2^{11}) – (2 + 2^2 + … + 2^{10})`

   `-> A = 2^{11} – 2`

   `-> A = 2046`

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   `B = 1/(1 . 2) + 1/(2 . 3) + … + 1/(9 . 10)`

   `-> B = 1 – 1/2 + 1/2 – 1/3 + …. + 1/9 – 1/10`

   `-> B = 1 + (- 1/2 + 1/2 – 1/3 + …. + 1/9) – 1/10`

   `-> B = 1 – 1/10`

   `-> B = 10/10 – 1/10 = 9/10`

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   Ta có : 

   `2046 = (2046 . 10)/(1 . 10) = 20460/10`

   `9/10`

   `-> 20460/10 > 9/10`

   hay `2046 > 9/10`

   `-> A > B`

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