Let's compare and in order to find whether the sequence is monotonic or not:
Since is always positive, we need to evaluate the sign of the quadratic expression in order to evaluate the sign of the expression. For this, we need to find the zeros:
Therefore, for , that is for every . Therefore, for an arbitrary , we have:
so the sequence is decreasing. That's why it is bounded by its first term:
To examine whether the sequence is bounded below, notice that it has a limit:
Therefore, the sequence is decreasing and is bounded by 0 and .