A = 11/2(1/2)2 ( 1/2)3 ( 1/2)4 ( 1/2)5 ..... ( 1/2)2021 chứng minh a = 2- (1/2) 2021

Question

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

tonhitruc · Answer

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}

ngocbichchau · Answer

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)    @lienlien55098

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

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