Question 62
Sequence $\{a_n\}$ is defined by:
$$
a_0 = \frac{1}{2},\ a_{n+1} = a_n + \frac{a_n^2}{2012},\ n = 0, 1, \dots
$$
Find the integer $k$ such that $a_k \lt 1 \lt a_{k+1}$.
$$
a_0 = \frac{1}{2},\ a_{n+1} = a_n + \frac{a_n^2}{2012},\ n = 0, 1, \dots
$$
Find the integer $k$ such that $a_k \lt 1 \lt a_{k+1}$.