Thaddeus Function
Algebra
Level
4
Let
\[f(n) = \frac {1}{ \sqrt{1} + \sqrt{2}} + \frac {1}{\sqrt{2} + \sqrt{3}} + \frac {1}{\sqrt{3} + \sqrt{4}} \ldots \frac{1}{\sqrt{n}+\sqrt{n+1}}. \]
For how many positive integers \(n\), in the range \(1 \leq n \leq 1000 \), is \(f(n)\) an integer?
This problem is posed by Thaddeus A.
by
Mei Li