Question

[Đặng Khánh Linh]

A = 1/2 + 1/4 + 1/8+ ......+ 1/ 512 + 1/1024

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Answer 1

[Bùi Thế Hào]

Ta có: \(\frac{1}{2}=1-\frac{1}{2}\);

\(\frac{1}{4}=\frac{1}{2}-\frac{1}{4}\); \(\frac{1}{8}=\frac{1}{4}-\frac{1}{8}\);...; \(\frac{1}{512}=\frac{1}{256}-\frac{1}{512}\); \(\frac{1}{1024}=\frac{1}{512}-\frac{1}{1024}\)

=> \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}+\frac{1}{1024}\)

=> \(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{256}-\frac{1}{512}+\frac{1}{512}-\frac{1}{1024}\)

=> \(A=1-\frac{1}{1024}=\frac{1023}{1024}\)

Đáp số: \(A=\frac{1023}{1024}\)