\(B=512-\dfrac{512}{2}-\dfrac{512}{2^2}-....-\dfrac{512}{2^{10}}\)
\(=512-\left(\dfrac{512}{2}+\dfrac{512}{2^2}+....+\dfrac{512}{2^{10}}\right)\)
\(=512-\left[512\left(\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{10}}\right)\right]\)
Đặt \(A=\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{10}}\)
\(2A=1+\dfrac{1}{2}+...+\dfrac{1}{2^9}\)
\(\Rightarrow2A-A=1-\dfrac{1}{2^{10}}\)
\(\Rightarrow A=1-\dfrac{1}{2^{10}}\)
\(\Rightarrow B=512-\left(512.A\right)=512-\left[512.\left(1-\dfrac{1}{2^{10}}\right)\right]\)
\(=512-512.\dfrac{1023}{1024}=512-\dfrac{1023}{2}=\dfrac{1}{2}\)