12.觀察規律:
$\begin{array}{l}\frac{1}{{\sqrt{2}+1}}=\frac{{\sqrt{2}-1}}{{({\sqrt{2}+1})({\sqrt{2}-1})}}=\frac{{\sqrt{2}-1}}{2-1}=\sqrt{2}-1\end{array}\begin{array}{l}$
$\frac{1}{{\sqrt{3}+\sqrt{2}}}=\frac{{\sqrt{3}-\sqrt{2}}}{{({\sqrt{3}+\sqrt{2}})({\sqrt{3}-\sqrt{2}})}}=\frac{{\sqrt{3}-\sqrt{2}}}{3-2}=\sqrt{3}-\sqrt{2}\end{array}$
同理可得:$\begin{array}{l}\frac{1}{{\sqrt{4}+\sqrt{3}}}=\sqrt{4}-\sqrt{3}\end{array}$
依照上述規律,則:$\frac{1}{{\sqrt{11}+\sqrt{10}}}$=$\sqrt{11}$-$\sqrt{10}$; $\frac{1}{{\sqrt{n+1}+\sqrt{n}}}$=$\sqrt{n+1}$-$\sqrt{n}$(n≥1的整數);
$({\frac{1}{{\sqrt{2}+1}}+\frac{1}{{\sqrt{3}+\sqrt{2}}}+\frac{1}{{\sqrt{4}+\sqrt{3}}}+…+\frac{1}{{\sqrt{2016}+\sqrt{2015}}}})({\sqrt{2016}+1})$=2015.