Reciprocal Radical Sum
Problem
Consider the following series.
$$S(n) = \dfrac{1}{\sqrt{1} + \sqrt{2}} + \dfrac{1}{\sqrt{2} + \sqrt{3}} + \dfrac{1}{\sqrt{3} + \sqrt{4}} + ... + \dfrac{1}{\sqrt{n} + \sqrt{n+1}}$$For which values of $n$ is $S(n)$ rational?
Problem ID: 266 (05 Feb 2006) Difficulty: 4 Star