Question

-1-1/2-1/4-1/8-...-1/1024 giúp với giải chi tiết nha

Answer 1

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

\(\Rightarrow-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{1024}\)

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

\(=-2+1-1+\frac{1}{2}-\frac{1}{2}+\frac{1}{4}-...-\frac{1}{512}+\frac{1}{1024}\)

\(=-2+\frac{1}{1024}\)

\(=-\frac{2047}{1024}\)