The study of (infinite) series is widely regarded as the most difficult topic in all of calculus.  The idea of "adding up" an infinite number of terms and the "sum of the series" being a finite number sometimes and not a finite number other times seems to boggle the imagination.  

Sequences seem to be manageable, since the terms of an (infinite) sequence either approach a number (the limit) sufficiently or don't approach a number sufficiently, as n goes to infinity.  Our experience with limits of functions extends well to sequences.

The convergence of series to a sum is defined in terms of the convergence of sequences to a limit.  Clarifying the dual use of the word "converge" in the previous sentence is key in your success in dealing with series.  To determine convergence of series, you must master the concepts sequences.

• Use various sequence tests to determine the convergence and divergence of infinite sequences.
• Use various series tests to determine the convergence and divergence of infinite series.