Question 19
Suppose that $a_1 = 2$ and the sequence $(a_n)$ satisfies the recurrence relation
$$
\frac{a_n - 1}{n - 1} = \frac{a_{n-1} + 1}{(n-1) + 1}
$$
for all $n \ge 2$. What is the greatest integer less than or equal to
$$
\sum_{n=1}^{100} a_n^2?
$$
$$
\frac{a_n - 1}{n - 1} = \frac{a_{n-1} + 1}{(n-1) + 1}
$$
for all $n \ge 2$. What is the greatest integer less than or equal to
$$
\sum_{n=1}^{100} a_n^2?
$$