Covered today: Basic definitions associated with sequences and
series. Definition of convergence, divergence, conditional convergence.
Geometric series, p-series. Tests for convergence/divergence.
For next time:
- 1.
- Let
.
Compute ,
and
prove
your answer using the definition of convergence.
- 2.
- Prove, using the definition of divergence, that if
,
then an diverges to .
- 3.
- Using the defintion of convergence, prove the following: Let an
and
bn be sequences and define cn = an+bn. If
and
,
then
.
- 4.
- Assume that -1 < r < 1, and consider the geometric series
.
Write down the nth partial sum Sn.
Prove that
.
Prove that the series
converges to .
- 5.
- Compute
- 6.
- Compute
- 7.
- Compute
- 8.
- Determine whether each of the following series converges or
diverges
- 9.
-
Math 23 Fall 1999
1999-11-02