Question 166
The sequence of real numbers $(a_n)$ is defined by
$$
a_1 = 5 \quad \text{and} \quad a_n = \sqrt[n]{a_{n-1}^{n-1} + 2^{n-1} + 2 \cdot 3^{n-1}} \quad \text{for all } n \ge 2.
$$
Prove that the sequence $(a_n)$ is decreasing.
$$
a_1 = 5 \quad \text{and} \quad a_n = \sqrt[n]{a_{n-1}^{n-1} + 2^{n-1} + 2 \cdot 3^{n-1}} \quad \text{for all } n \ge 2.
$$
Prove that the sequence $(a_n)$ is decreasing.