\(B=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+.......+\dfrac{1}{2^{2017}}\)
\(\Leftrightarrow2B=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+............+\dfrac{1}{2^{2016}}\)
\(\Leftrightarrow2B-B=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+..........+\dfrac{1}{2^{2016}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+........+\dfrac{1}{2^{2017}}\right)\)
\(\Leftrightarrow B=1-\dfrac{1}{2^{2017}}\)