阅读并完成下面问题：
①$\dfrac{1}{1+\sqrt{2}}=\dfrac{1×(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\sqrt{2}-1$；
②$\dfrac{1}{\sqrt{3}+\sqrt{2}}=\dfrac{1×(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}=\sqrt{3}-\sqrt{2}$；
③$\dfrac{1}{\sqrt{5}+2}=\dfrac{1×(\sqrt{5}-2)}{(\sqrt{5}+2)(\sqrt{5}-2)}=\sqrt{5}-2$；…
$(1)$填空：$\sqrt{7}+\sqrt{6}$的倒数为 ______$.\dfrac{1}{\sqrt{n+1}+\sqrt{n}}(n$为正整数$)$的值为 ______.
$(2)$计算：$\dfrac{1}{\sqrt{2}+1}+\dfrac{1}{\sqrt{3}+\sqrt{2}}+\dfrac{1}{\sqrt{4}+\sqrt{3}}+…+\dfrac{1}{\sqrt{100}+\sqrt{99}}.$