Question 3
Let $(a_n)$ be the sequence such that $a_1 = \frac{3}{2}$ and
$$
a_{n+1} = a_n - \frac{3n+2}{2n(n+1)(2n+1)},\ n \ge 1.
$$
Find the limit $\lim_{n \to +\infty} a_n$.
$$
a_{n+1} = a_n - \frac{3n+2}{2n(n+1)(2n+1)},\ n \ge 1.
$$
Find the limit $\lim_{n \to +\infty} a_n$.