Limit and Series

Consider the series  and its associated sequence of partial sums  . We will say that  is convergent if and only if the sequence  is convergent. The total sum of the series is the limit of the sequence , which we will denote by


So as you see the convergence of a series is related to the convergence of a sequence. Many do some serious mistakes in confusing the convergence of the sequence of partial sums  with the convergence of the sequence of numbers  .
Basic Properties.

1.