Ta xét bài toán tổng quát sau:$\frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{\sqrt{n+1}-\sqrt{n}}{(\sqrt{n+1}+\sqrt{n})(\sqrt{n+1}-\sqrt{n})}=\sqrt{n+1}-\sqrt{n}$
$\rightarrow A=\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+...+\sqrt{2013}-\sqrt{2012}=\sqrt{2013}-\sqrt{1}=\sqrt{2013}-1$