At the end of this section, students should be able to:

1. use the summation, \(\sum\), notation;
2. define a series, as the sum of the terms of a sequence;
3. identify the \(n\)th term of a series, in the summation notation;
4. define the \(m\)th partial sum \(S_m\) as the sum of the first \(m\) terms of the sequence, that is,
\(\displaystyle S_m=\sum_{r=1}^m a_r\)
5. apply mathematical induction to establish properties of series;
6. find the sum to infinity of a convergent series;
7. apply the method of differences to appropriate series, and find their sums;
8. use the Maclaurin theorem for the expansion of series;
9. use the Taylor theorem for the expansion of series.