4. 观察下列计算结果：
$\frac{1}{1 + \sqrt{2}} = -1 + \sqrt{2}$，
$\frac{1}{\sqrt{2} + \sqrt{3}} = -\sqrt{2} + \sqrt{3}$，
$\frac{1}{\sqrt{3} + \sqrt{4}} = -\sqrt{3} + \sqrt{4}$，
$\vdots$
$\frac{1}{\sqrt{2014} + \sqrt{2015}} = -\sqrt{2014} + \sqrt{2015}$.
(1) 写出$\frac{1}{1 + \sqrt{2}} = -1 + \sqrt{2}$的化简过程；
(2) 根据上面的规律，写出第$n$个式子并验证；
(3) 利用上面的规律计算：
$(\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \cdots + \frac{1}{\sqrt{2014} + \sqrt{2015}})(1 + \sqrt{2015})$.

(1)$\frac{1}{\sqrt{2}+1}=\frac{1\cdot(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\frac{\sqrt{2}-1}{1}=\sqrt{2}-1$ (2)$\frac{1}{\sqrt{n}+\sqrt{n + 1}}=-\sqrt{n}+\sqrt{n + 1}$,略 (3)$(\sqrt{2}-1+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\cdots+\sqrt{2015}-\sqrt{2014})\cdot(1+\sqrt{2015})=(\sqrt{2015}-1)(\sqrt{2015}+1)=2014$