Ta có: \(-1-\frac{1}{2}-\frac{1}{4}-....-\frac{1}{1024}\)
= \(1+\left(\frac{1}{2}+\frac{1}{4}+.....+\frac{1}{1024}\right)\)
= \(1+2.\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}\right)\)
= \(1+\left(1+\frac{1}{2}+\frac{1}{4}+....+\frac{1}{512}\right)\)
= \(1+\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}\right)+\left(\frac{1}{2}+....+\frac{1}{1024}\right)\)
= \(1+\left(1+\frac{1}{1024}\right)\)
\(=\frac{2049}{1024}\)
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