A = 1+1/2+(1/2)^2 + ( 1/2)^3 + ( 1/2)^4 + ( 1/2)^5 +…..+ ( 1/2)^2021 chứng minh a = 2- (1/2) ^2021

2 bình luận về “A = 1+1/2+(1/2)^2 + ( 1/2)^3 + ( 1/2)^4 + ( 1/2)^5 +…..+ ( 1/2)^2021 chứng minh a = 2- (1/2) ^2021”

1. A = 1 + 1/2 + ( 1/2 )^2 + ( 1/2 )^3 + … + ( 1/2 )^{2021}

   => 2A = 2 + 1 + 1/2 + ( 1/2 )^2 + … + ( 1/2 )^{2020}

   => 2A – A = ( 2 + 1 + 1/2 + ( 1/2 )^2 + … + ( 1/2 )^{2020} ) –

   ( 1 + 1/2 + ( 1/2 )^2 + ( 1/2 )^3 + … + ( 1/2 )^{2021} )

   => A = 3 – 1 – ( 1/2 )^{2021}

   => A = 2 – ( 1/2 )^{2021}

   Vậy : A = 2 – ( 1/2 )^{2021}

    

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2. 2A=2+1+1/2+(1/2)^2+…+(1/2)^2020

   2A-A=2+1+1/2+(1/2)^2+…+(1/2)^2020-1-1/2-(1/2)^2-…-(1/2)^2021

   A=2-(1/2)^2021 (đpcm)

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