What is the simplified value of $$\frac{1}{\sqrt{7}-\sqrt{16}}-\frac{1}{\sqrt{16}-\sqrt{15}}+\frac{1}{\sqrt{15}-\sqrt{14}}-\frac{1}{\sqrt{14}-\sqrt{13}}+\frac{1}{\sqrt{13}-\sqrt{12}}$$

Expression : $$\frac{1}{\sqrt{17}-\sqrt{16}}-\frac{1}{\sqrt{16}-\sqrt{15}}+\frac{1}{\sqrt{15}-\sqrt{14}}-\frac{1}{\sqrt{14}-\sqrt{13}}+\frac{1}{\sqrt{13}-\sqrt{12}}$$

Rationalizing the denominator, we get :

= $$(\frac{1}{\sqrt{17}-\sqrt{16}}\times\frac{\sqrt{17}+\sqrt{16}}{\sqrt{17}+\sqrt{16}})-(\frac{1}{\sqrt{16}-\sqrt{15}}\times\frac{\sqrt{16}+\sqrt{15}}{\sqrt{16}+\sqrt{15}})+(\frac{1}{\sqrt{15}-\sqrt{14}}\times\frac{\sqrt{15}+\sqrt{14}}{\sqrt{15}+\sqrt{14}})-(\frac{1}{\sqrt{14}-\sqrt{13}}\times\frac{\sqrt{14}+\sqrt{13}}{\sqrt{14}+\sqrt{13}})+(\frac{1}{\sqrt{13}-\sqrt{12}}\times\frac{\sqrt{13}+\sqrt{12}}{\sqrt{13}+\sqrt{12}})$$

Using, $$(a+b)(a-b)=a^2-b^2$$

= $$(\frac{(\sqrt{17}+\sqrt{16})}{(17-16)})-(\frac{(\sqrt{16}+\sqrt{15})}{(16-15)})+(\frac{(\sqrt{15}+\sqrt{14})}{(15-14)})-(\frac{(\sqrt{14}+\sqrt{13})}{(14-13)})+(\frac{(\sqrt{13}+\sqrt{12})}{(13-12)})$$

= $$\sqrt{17}+\sqrt{16}-\sqrt{16}-\sqrt{15}+\sqrt{15}+\sqrt{14}-\sqrt{14}-\sqrt{13}+\sqrt{13}+\sqrt{12}$$

= $$\sqrt{17}+\sqrt{12}$$

=> Ans - (C)