This preview shows pages 1–3. Sign up to view the full content.
Lecture 23: Series Summary
It would not be wise to apply tests for convergence
in a speci±c order to ±nd one that ±nally works.
Instead, a proper stretegy, as with integration, is
to classify the series according to its form. Keep
in mind that a conclusion about the convergence
of a series sometimes can be reached in di²erent
ways.
1. ’easier cases’: If a series is of the form of
p
±
series, geometric series or telescoping series,
their convergence properties are known. In fact,
the de±nite sum of a geometric series or a tele
scoping series can be found if it is convergent.
2. If a series has a form similar to the ’easier
cases’, then one of the comparison tests should
be considered. For instance, if
a
n
is a rational or
algebraic expression (contains roots of polynomi
als), then the series should be compaired with a
p
±
series.
3. It is always easier to see if the necessary con
dition for convergence is met than to check if the
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documentseries is convergent. If lim
a
n
6
= 0, then the series
is divergent by Test for Divergent.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Bonner
 Calculus

Click to edit the document details