## SERIES

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.