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Math Words
Math Words: Alternating Series Test
This site begins with the general form of an alternating series and then gives an easy to follow discussion of how to determine if an alternating series is convergent.
Math Open Reference
Math Open Reference: Alternating Series Test
Learn about the alternating series test with this helpful reference tool. Provides a detailed definition and examples that enhance further explanation. Includes links to related topics.
Math Medics
S.o.s. Math: Sequences Limits
This lesson discusses the limit of a sequence in mathematics. Compares convergent and divergent sequences and presents numerical and graphical examples.
Wolfram Research
Wolfram Math World: Radius of Convergence
MathWorld provides a site about the Radius of Convergence. Brief and factual, formulas are provided along with several links to additional information on related subjects.
Wolfram Research
Wolfram Math World: Convergence Tests
This page provides links to information about tests to determine the convergence or divergence of a series. No information about convergence tests is offered directly at this link.
Other
Old Dominion University/ the Alternating Series Test
This site provides the equation for the alernating series test.
Wolfram Research
Wolfram Math World: Divergent Series
This page discusses divergent series, providing links to more detailed information about various aspects of divergent series.
Other
Lake Tahoe Community College
This site offers a clear definition of what a Power Series is and clearly discusses the radius of Convergence using the ratio test through clear examples.
Wolfram Research
Wolfram Math World: Integral Test
This page gives a brief statement of the Integral Test for convergent or divergent series. This test is also called the Cauchy Integral Test or the Maclaurin Integral Test.
Texas Instruments
Texas Instruments: Ratio Test
This activity will demonstrate the use of the ratio test to discuss the convergence of an infinite series.
Wolfram Research
Wolfram Math World: Convergent Sequence
This site from MathWorld explains convergent sequences with links to related information. The information is very brief, but examples and formulas are provided.
Wolfram Research
Wolfram Math World: Divergence Test
This is a brief statement of a divergence test that can be used to determine whether or not a given series converges or diverges. Provides no explanation, but simply a statement.
Wolfram Research
Wolfram Math World: Leibniz Criterion
This page states the Leibniz Criterion, or the alternating series test that determines whether or not an alternating series converges.
Mathematics Archives
Math Archives: Visual Calculus: Ratio Test
Visual Calculus offers a discussion and exercises concerning the ratio test for convergence of series.
Mathematics Archives
Math Archives: Visual Calculus: Integral Test
Visual Calculus offers a discussion and exercises concerning the integral test for convergence of series. The site also discusses the power series test.
Wolfram Research
Wolfram Math World: Ratio Test
This page states the Ratio Test for convergent or divergent series, sometimes called the Cauchy Ratio Test or the d'Alembert Ratio Test. Brief but informational.
Virginia Commonwealth University
Don Mikulecky: The Limit of a Sequence
A series of slides discussing the mathematical limit of a sequence. The slideshow is straight-forward, providing terminology and examples of how to find sequence limits. The slideshow goes on to discuss series, and more.
Wolfram Research
Wolfram Math World: Sine
MathWorld provides graphs of the sine function, both 2-dimensional and 3-dimensional. Higher level mathematical applications given, including the hyperbolic sine function, representation of the sine function as an infinite sum as well as...
Shodor Education Foundation
Shodor Interactivate: Tortoise and Hare Race
Step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence of an infinite sequence of numbers.
Math Medics
S.o.s. Math: Sequences: Special Limits
This lesson discusses important limits of particular sequences that can be very "useful in many branches of science." Includes good proofs.
Math Medics
S.o.s. Math: Ratio Test
This a comprehensive tutorial explaining the Ratio Test with examples the students can work.
Math Open Reference
Math Open Reference: Integral Test
A handy reference guide to the integral test. It provides definitions, examples, and an animation that enhances further explanation. Includes links to related topics.
Math Words
Math Words: Root Test
Math Word briefly states the root test and discusses when the series is convergent, divergent or does not exist.