Series - Convergence/Divergence

In the earlier section we spent some time getting familiar with series and we briefly explained convergence and divergence.  Previous to worrying as regards convergence and divergence of a series we wanted to ensure that we've started to get comfortable with the notation included in series and some of the several manipulations of series that we will, on occasion, require to be able to do.

As noted in the earlier section most of what we were doing there won't be done much more in this section. Thus, it is now time to start talking about the convergence and divergence of a series as this will be a topic which we'll be dealing with to one extent.

Thus, let us remind just what an infinite series is and what it means for a series to be convergent or divergent. We will start along with a sequence {a_n}_n=1^∞ and again note that we're starting the sequence at n = 1 just only for the sake of convenience and it can, actually, be anything. Next we illustrate the partial sums of the series as and these make a new sequence, {s_n}^∞ _n=1