Lesson 11

Problem. Let the probabilities of \(2n+1\) symbols be \[\frac{1}{3}, \frac{1}{3}, \frac{1}{9}, \frac{1}{9}, \dotsc, \frac{1}{3^{n}}, \frac{1}{3^{n}}, \frac{1}{3^{n}}.\] What does its entropy approach as \(n \to \infty\)?