\(\text{Ta có: }\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-....-\frac{1}{1024}\)
\(=\left(1-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{4}\right)-\left(\frac{1}{4}-\frac{1}{8}\right)-......-\left(\frac{1}{512}-\frac{1}{1024}\right)\)
\(=1-\frac{1}{1024}\)
\(=\frac{1023}{1024}\)