Let \( S = \mathbb{N} \cup \{0\} \). Define a relation \( R \) from \( S \) to \( \mathbb{R} \) by: \( R = \{(x, y): \lo…

Let \( S = \mathbb{N} \cup \{0\} \). Define a relation \( R \) from \( S \) to \( \mathbb{R} \) by: \( R = \{(x, y): \log_e y = x \log_e \left(\frac{2}{5}\right),\ x \in S, y \in \mathbb{R}\} \). Then, the sum of all the elements in the range of \( R \) is equal to: