question_answer

Let\[S=\frac{\sqrt{1}}{1+\sqrt{1}+\sqrt{2}}+\frac{\sqrt{2}}{1+\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}+\sqrt{4}}\]\[+...+\frac{\sqrt{n}}{1+\sqrt{n}+\sqrt{n+1}}=3.\]  Then n is equal to_______.

Answer:

8