Series
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Lesson Summary:
In this lesson on series, we learn about infinite series, partial sums, and convergent and divergent series. We
Lesson Description:
Sequences of partial sums. Geometric series and the harmonic series.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
Questions answered by this video:
- What are infinite series?
- What is the difference between a sequence and a series?
- When does a series converge and diverge?
- What is the sum of the series 1/k(k + 1)?
- What is a partial fraction expansion of a series?
- What is a telescoping series?
- How do you find the sum of a telescoping series?
- What is a sequence of partial sums?
- What is a geometric series?
- How do you find the sum of a geometric series?
- What is the formula for the sum of a geometric series?
- When does the sum of x^k = 1/(1 - x) and when does the sum of x^k diverge?
- What is the sum of 2^k/3^k?
- What is the sum of (-1)^k/2^k?
- What are the arithmetic properties of convergence for series?
- What is the sum of 1/3^k?
- What is index shifting?
- What are basic tests for divergence of series?
- What is the sum of 1/k from k = 1 to infinity?
- What is the harmonic series?
- Does a series converge if its terms approach 0?
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Staff Review
This video describes infinite series from the definition of a sequence. Many examples are given. Techniques for finding the sum of these series are explained. Geometric series are then introduced and their sum is found. Basic tests for divergence are explaining and the harmonic and telescoping series are defined and explained.
