I have a rather general question about sequences:
How do you determine whether it is appropriate to find an upper or lower bound of a sequence? In particular, suppose $a_n = \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{p_n}$ where $p_n$ denotes the $n^{th}$ prime. How do I know whether to bound the sequence from above or below?