Question 86
Define the sequence $x_1, x_2, \dots$, by $x_1 = \frac{1}{6}$ and
$$
x_{n+1} = \frac{n+1}{n+3} \left( x_n + \frac{1}{2} \right),
$$
for every $n \ge 1$. Find $x_{2011}$.
$$
x_{n+1} = \frac{n+1}{n+3} \left( x_n + \frac{1}{2} \right),
$$
for every $n \ge 1$. Find $x_{2011}$.