The sum of the infinite series \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{2}} \right)+{{\sin }^{-1}}\left( \frac{\sqrt{2}-1}{\sqrt{6}} \right)+{{\sin }^{-1}}\left( \frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}} \right)+...\]\[+...+{{\sin }^{-1}}\left( \frac{\sqrt{n}-\sqrt{(n-1)}}{\sqrt{\{n(n+1)\}}} \right)+...\] is

• A. \[\frac{\pi }{8}\]
• B. \[\frac{\pi }{4}\]
• C. \[\frac{\pi }{2}\]
• D. \[\pi \]