tính nhanh: A=1/2+1/2^2+1/2^3+…….+1/2^10

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1. Đáp án:

   `A=1/2+1/2^2+1/2^3+…….+1/2^10=1023/1024`

   Giải thích các bước giải:

   `A=1/2+1/2^2+1/2^3+…….+1/2^10`
   `2A=1+1/2+1/2^2+…+1/2^9`
   `2A-A=(1+1/2+1/2^2+…+1/2^9)-(1/2+1/2^2+1/2^3+…+1/2^10)`
   `A=1+1/2+1/2^2+…+1/2^9-1/2-1/2^2-1/2^3-…-1/2^10`
   `A=1+(1/2-1/2)+(1/2^2-1/2^2)+…+(1/2^9-1/2^9)-1/2^10`
   `A=1-1/2^10`
   `A=1-1/1024`
   `A=1024/1024-1/1024`
   `A=1023/1024`

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2. `A = 1/2 + 1/2^2 + 1/2^3 + … + 1/2^10`

   `⇒ 2A = 1 + 1/2 + 1/2^2 + … + 1/2^9`

   `⇒ 2A – A = 1 – 1/2^10`

   `⇒ A = (2^10 – 1)/2^10`

   `⇒ A = 1023/1024`

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