Question 153
Let the sequence $(a_n)_{n \in N^*}$ be given with $a_1 = 2$ and $a_{n+1} = a_n^2 - a_n + 1$. Find the minimum real number $L$ such that for every $k \in N^*$
$$
\sum_{i=1}^{k} \frac{1}{a_i} \lt L.
$$
$$
\sum_{i=1}^{k} \frac{1}{a_i} \lt L.
$$