My math teacher gave us this exercise for homework:
Given $ a \in [-3, \infty), $ a given sequence $(x_n),$ with $ x_n = \left(\frac{a^n+2}{3^n+4}\right)$
Determine $a$ so that the sequence $(x_n)$ is convergent.
I wrote that if $a$ is negative $(<0)$ the sequence is not monotone anymore, so according to Monotone Convergence Theorem, the sequence cannot be convergent because it isn't monotone. However, the answer at the end of the book is $x \in (-3, 3]$ which kinda mesmerized me...
Any thoughts on the correctitude of the "official" answer provided by the book?