Đặt \(A=\frac24+\frac68+\frac{14}{16}+\cdots+\frac{2046}{2048}\)
\(=1-\frac24+1-\frac28+\ldots+1-\frac{2}{2048}\)
\(=1-\frac12+1-\frac14+\cdots+1-\frac{1}{1024}\)
\(=10-\left(\frac12+\frac14+\cdots+\frac{1}{1024}\right)\)
Đặt \(B=\frac12+\frac14+\cdots+\frac{1}{1024}\)
=>\(2\times B=1+\frac12+\cdots+\frac{1}{512}\)
=>\(2\times B-B=1+\frac12+\cdots+\frac{1}{512}-\frac12-\frac14-\cdots-\frac{1}{1024}\)
=>\(B=1-\frac{1}{1024}=\frac{1023}{1024}\)
Ta có: \(A=10-\left(\frac12+\frac14+\cdots+\frac{1}{1024}\right)\)
\(=10-\frac{1023}{1024}=\frac{10240-1023}{1024}=\frac{9217}{1024}\)
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