# 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).

## 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