Tính : E = 1 + 3 / 2^3 + 4 / 2^4 + 5 / 2^5 + … + 100 / 2^100 vinh6adck mô rồi

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1. Đáp án:

    

   A=1+3/2^3+4/2^4+5/2^5+…100/2^100
   1/2*A = 1/2 + 3/2^4 + 4/2^5 +….+ 99/2^100 + 100/2^101

   A- A/2 = 1/2A =1/2 + 3/2^3 + 1/2^4 +…+1/2^100 – 100/2^101=

   = [1/2+1/2^2 +1/2^3 +…+1/2^100] -100/2^101 (Do 3/2^3 = 1/2^2 +1/2^3)

   =[1-(1/2)^101]/(1-1/2) -100/2^101 = 

   =(2^101 -1)/2^100 – 100/2^101

   => A= (2^101 -1)/2^99 – 100/2^100

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