Ta có: \(B=\dfrac{1+2+2^2+2^3+...+2^{2014}}{1-2^{2015}}\)
\(\Rightarrow2B=\dfrac{2+2^2+2^3+2^4+...+2^{2015}}{1-2^{2015}}\)
\(\Rightarrow2B-B=\dfrac{2+2^2+2^3+2^4+...+2^{2015}}{1-2^{2015}}-\dfrac{1+2+2^2+2^3+...+2^{2014}}{1-2^{2015}}\)
\(\Rightarrow B=\dfrac{2^{2015}-1}{1-2^{2015}}=-1\)
Vậy \(B=-1\).