Find the value of the expression $\sqrt{1+2011^{2}+\left(\frac{2011}{2012}\right)^{2}}+\frac{2011}{2012}$.
The expression under the square root is $\quad\left(2011^{2}+2 \cdot 2011+1\right)-2 \cdot 2011+\left({ }^{2011} / 2012\right)^{2}=2012^{2}-2 \cdot 2012 \cdot 2011 / 2012+$

$\left({ }^{2011} / 2012\right)^{2}=(2012-2011 / 2012)^{2}$, so the original expression equals $(2012-2011 / 2012)+{ }^{2011} / 2012=2012$.

## Answer

2012.