Determine all positive integers $n$ for which the number \[ N = \frac{1}{n \cdot (n + 1)} \]can be represented as a finite decimal fraction.
Source: Romania National Olympiad 2023
Tags: algebra, periodic decimal number
Determine all positive integers $n$ for which the number \[ N = \frac{1}{n \cdot (n + 1)} \]can be represented as a finite decimal fraction.