Question

 tính : 1 + 1/2 + 1/4 + 1/8 + ...+ 1/128 +1/256

viết cách giải cho mính nhé.mính click cho

 

Answer 1

Đặt \(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+...+\frac{1}{128}-\frac{1}{256}\)

\(\Rightarrow A=1-\frac{1}{256}\)

\(\Rightarrow A=\frac{255}{256}\)

Answer 2

Ta có: A = 1 + 1/2 + 1/4 + 1/8 + ... + 1/128 + 1/256

              =  1 + 1/2 + 1/2² + 1/2³ + ... + 1/2⁷ + 1/2⁸

   => 2A = 2 + 1 + 1/2 + 1/2³ + .... + 1/2⁶ + 1/2⁷

             = 2 - 1/2⁸ = 511/256

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