\(A=\sqrt[]{1+2015^2+\dfrac{2015^2}{2016^2}}+\dfrac{2015}{2016}\)
\(\Leftrightarrow A=\sqrt[]{\left(1+2015\right)^2-2.2015+\dfrac{2015^2}{\left(2015+1\right)^2}}+\dfrac{2015}{2016}\)
\(\Leftrightarrow A=\sqrt[]{\left(1+2015-\dfrac{2015}{2015+1}\right)^2}+\dfrac{2015}{2016}\)
\(\Leftrightarrow A=\left|1+2015-\dfrac{2015}{2016}\right|+\dfrac{2015}{2016}\)
\(\Leftrightarrow A=1+2015-\dfrac{2015}{2016}+\dfrac{2015}{2016}\)
\(\Leftrightarrow A=1+2015=2016\)
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