1/3 + 1/3^2 + 1/3^3 +……+ 1/3^2017+1/3^2018 so sánh với 1/2

1 bình luận về “1/3 + 1/3^2 + 1/3^3 +……+ 1/3^2017+1/3^2018 so sánh với 1/2”

1. Đặt A=1/3 + 1/3^2 + 1/3^3 +……+ 1/3^2017+1/3^2018

   => 3A=1+1/3 + 1/3^2 + 1/3^3 +……+ 1/3^2017

   => 3A-A=1+1/3 + 1/3^2 + 1/3^3 +……+ 1/3^2017-(1/3 + 1/3^2 + 1/3^3 +……+ 1/3^2017+1/3^2018)

   => 2A=1-1/3^2018

   => A=1/2-(1/3^2018 : 2) < 1/2

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