Question 21
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 $n\ge2.$ 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}
$$ for all $n\ge2.$ What is the greatest integer less than or equal to $$
\sum_{n=1}^{100}a_n^2?
$$