Question 79
Let $(a_n)$ be a sequence defined by
$$
a_0 = 9 \quad \text{and} \quad a_{k+1} = 3a_k^4 + 4a_k^3 \quad \text{for all } k \ge 0.
$$
Prove that the decimal representation of $a_{11}$ ends with at least 2011 digits 9.
$$
a_0 = 9 \quad \text{and} \quad a_{k+1} = 3a_k^4 + 4a_k^3 \quad \text{for all } k \ge 0.
$$
Prove that the decimal representation of $a_{11}$ ends with at least 2011 digits 9.