Question 2
The real sequence $(a_n)$ is defined by
$$a_1=5,\qquad a_n=\sqrt[n]{a_{n-1}^{n-1}+2^{n-1}+2\cdot3^{n-1}}\quad(n\ge2).$$
1. Find the general term of $(a_n)$.
2. Prove that $(a_n)$ is decreasing.
$$a_1=5,\qquad a_n=\sqrt[n]{a_{n-1}^{n-1}+2^{n-1}+2\cdot3^{n-1}}\quad(n\ge2).$$
1. Find the general term of $(a_n)$.
2. Prove that $(a_n)$ is decreasing.