Question 33
Given a sequence of real numbers $(x_n)$
$$
x_1 = 3 \quad \text{and} \quad x_n = \frac{n+2}{3n}(x_{n-1} + 2), \quad \forall n \ge 2.
$$
Prove that the sequence has a finite limit as $n \to \infty$ and calculate this limit.
$$
x_1 = 3 \quad \text{and} \quad x_n = \frac{n+2}{3n}(x_{n-1} + 2), \quad \forall n \ge 2.
$$
Prove that the sequence has a finite limit as $n \to \infty$ and calculate this limit.