Question 21
Suppose $a_1 = 4$ and $a_{n+1} \ge a_n + n + 2$ for all natural numbers $n$. Show that
$$
\frac{1}{a_1} + \frac{1}{a_2} + \dots + \frac{1}{a_{2010}} \lt \frac{3}{2}.
$$
$$
\frac{1}{a_1} + \frac{1}{a_2} + \dots + \frac{1}{a_{2010}} \lt \frac{3}{2}.
$$