An example.
We obtain the sequence of partial sums {s_{n}}.
An interactive example illustrating the difference between the sequence of terms and the sequence of partial sums.
is convergent if the sequence s_{n} is convergent and has finite limit. If
then we write
If the sequence s_{n} is not convergent then we say that the series
is divergent.
Properties of convergent series.
Convergence of geometric series. Discussion [Using Flash] [Using Java]
Example.
is convergent, then
Equivalently, if
then the series is divergent.
Discussion.
Examples.
Telescoping series.
Drill Problems.