The image contains four sequences $u_n$ that are defined for $n \geq 0$, and the task is to determine their monotonicity (whether they are increasing, decreasing, etc.). Here is a breakdown of each sequence:

1) Sequence 1:

$u_n = n^3 + 9n$ We need to determine the monotonicity of this function.

2) Sequence 2:

$u_n = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n} \quad (n \geq 0)$ This is a harmonic series, and we are tasked with determining whether it increases or decreases.

3) Sequence 3:

$u_n = \frac{n + 1}{2^n} \quad (n \geq 0)$ Here, the behavior of the sequence involves both $n$ and powers of 2, so we will analyze its monotonicity.

4) Sequence 4:

The recurrence relation: