4587 views, 3 ratings - 00:30:08
Part of video series Sequences
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.
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Sequences; the graph of a sequence; the limit of a sequence; the squeeze theorem. Some special sequences and their limits.
- What is a sequence?
- What is brace notation?
- What is a factorial sequence?
- What is the nth term of a sequence?
- How do you find the nth term of a sequence?
- How do you graph a sequence?
- How do you find the limit of a sequence?
- What is the squeeze theorem?
- How can you tell if a sequence converges?
- When is a sequence convergent or divergent?
- What are infinite limits of sequences?
- What are properties of limits?
- What is the limit of 1/n^p as n goes to infinity?
- What is the limit of x^n as n goes to infinity?
- What is the limit of x^1/n as n goes to infinity?
- What is the limit of n^1/n as n goes to infinity?
- How do you prove that the limit as n goes to infinity of (1 + x/n)^n = e^x?
- Why does the limit as n goes to infinity of (1 + 1/n)^n = e?
- What is growth rate comparison for limits?
- What is big Oh notation?
This video starts off very simply by defining a sequence and showing some very basic sequences. The brace form of the sequences is shown for several examples. The nth term is shown for some examples, as well as sequences’ graphs and their limits. The Squeeze Theorem and tests for convergence are also discussed. Several examples of divergent sequences are shown. The whole list of properties of limits of sequences is shown and explained. Some very famous / important limits are shown and some are proven. Big O or big oh notation is also explained, and the order of growth rates is shown. O (ln n) < O (n^1/q) < O (n^p) < O (x^n) < O (n!) < O (n^n).
The video was very helpful, clear and concise. I appreciate all the work that went behind making this video.