Đặt \(A=-\left(1+\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)
\(-2A=2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\)
\(-2A+A=2-\frac{1}{2^{10}}\)
\(\Leftrightarrow-A=2-\frac{1}{1024}=\frac{2047}{1024}\)
\(\Rightarrow A=-\frac{2047}{1024}\)
Vậy giá trị của biểu thức là -2047/1024
\(-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{1024}=-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)
Đặt \(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)
\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)
\(\Rightarrow2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
\(\Rightarrow2A-A=2-\frac{1}{2^{10}}\)
\(A=2-\frac{1}{2^{10}}\)
\(\Rightarrow-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{1024}=-\left(2-\frac{1}{2^{10}}\right)=-2+\frac{1}{2^{10}}\)
