Question

Tính:\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)

Answer 1

Gọi \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}\)

\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2014}\right)\)

\(\Rightarrow A=1-\frac{1}{1024}\)

\(\Rightarrow A=\frac{1023}{1024}\)

Vậy \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}=\frac{1023}{1024}\)