Question 151
Let $w_1 = a$, $w_2 = b$, and let the sequence of words ($w_n$) be defined recursively as follows:
$$
w_3 = ab, \quad w_4 = bab, \quad w_5 = abbab, \quad w_6 = bababbab, \dots,
$$
where each term is formed by concatenating the previous two terms, that is, $w_n = w_{n-2}w_{n-1}$ for all $n \ge 3$. Prove that for every $n \ge 3$, the word obtained by removing the first two letters from $w_n$ is a palindrome.
$$
w_3 = ab, \quad w_4 = bab, \quad w_5 = abbab, \quad w_6 = bababbab, \dots,
$$
where each term is formed by concatenating the previous two terms, that is, $w_n = w_{n-2}w_{n-1}$ for all $n \ge 3$. Prove that for every $n \ge 3$, the word obtained by removing the first two letters from $w_n$ is a palindrome.