The content of the image you uploaded appears to be a mathematical problem related to sequences and series. Here's a breakdown of the main problem components:

1. Given Recurrence Relation:
   The sequence $u_{n+1} = \frac{4u_n}{u_{n+2}}$ and the initial condition $u_0 = 4$ are provided.

2. Objective:
   Several steps are listed, such as:

   • Solve for specific values of $u_n$ given some initial conditions.
   • Find a formula for the sequence and prove the behavior of the sequence as $n \to \infty$.
   • Express the sequence $u_n$ as a limit function and determine its sum.

3. Steps & Equations:

   • You need to work through the recurrence, solve for $u_n$, and then determine the behavior of the sequence in the limit as $n \to \infty$.
   • The equation $v_n = \ln \left( \frac{u_n}{u_{n-2}} \right)$ is also given, indicating the transformation of the sequence for easier computation.

Would you like me to help with any specific part of this problem, such as deriving the sequence or solving for limits and sums?