Đặt \(A=\frac15+\frac{1}{10}+\frac{1}{20}+\frac{1}{40}+\cdots+\frac{1}{1280}\)
=>\(2\times A=\frac25+\frac15+\frac{1}{10}+\frac{1}{20}+\cdots+\frac{1}{640}\)
=>\(2\times A-A=\frac25+\frac15+\frac{1}{10}+\cdots+\frac{1}{640}-\frac15-\frac{1}{10}-\cdots-\frac{1}{1280}\)
=>\(A=\frac25-\frac{1}{1280}=\frac{512}{1280}-\frac{1}{1280}=\frac{511}{1280}\)