Question

1/2 + 1/4 + 1/8 + 1/16 + .......... + 1/2048

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Answer 1

\(\text{Đặt }S=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}.\)

\(\Rightarrow2S=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\)

\(\Rightarrow2S-S=S=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2048}\right)\)

\(\Rightarrow S=1-\frac{1}{2048}=\frac{2047}{2048}\)