# Vector Calculus Independent Study Path

## Unit 9: Infinite Series

In this unit, you will learn:
- What an infinite sequence is, and how to take its limit.
- The definition of an infinite series, and what it means for it
to converge or diverge.
- How to calculuate the value of a geometric series.
- The definition of a p-harmonic series.
- The limit test for the divergence of an infinite series.
- The comparison test.
- The integral test.
- The ratio test.
- The root test.
- The alternating series test.
- What a power series is, and how to find its radius and interval
of convergence.
- How to add, subtract, differentiate, and integrate power series,
and how to multiply one by a polynomial.
- How to find a power series approximation to a function near a
point (Taylor series).

The information on this page is available in Xdvi or PDF.
## Suggested Procedure

- Read and do some problems from
- Rogers Chapters 27 and 28, or
- Simmons Chapters 13 and 14.

- Take the Sample Test, Xdvi or PDF.
- Take a unit test.

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watko@athena.mit.edu
Last modified July 28, 1998