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Exercises

Concept of infinite series (Calculus) 
Computer 
Activity 

[1]

Experiment with series: find expressions for simple series, as well as using the technical definition of convergence.
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Solutions

Concept of infinite series (Calculus) 
Computer 
Activity 

[1]

Solutions to the series exercises.
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Exploring Infinite Series thro...

Concept of infinite series (Calculus)+ 
Sketchpad 
Activity 

[0]

This activity is an introduction to the concept of convergent infinite series using an iterative geometric construction. This activity has been adapted from the following article: Choppin, J. M. (1994...
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Absolute Convergence

Polynomial Approxs. and Series (Calculus) 
Computer 
Support Material 

[0]

Definitons of absolute and conditional convergence, and related tests for the convergence of an infinite series.
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Alternating Series

Altern. series, error bound. (Calculus) 
Computer 
Support Material 

[0]

Defines the Alternating Series Test and gives a way to calculate the error when approximating the sum of a series by a partial sum.
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Comparison Test

Comparison test (Calculus) 
Computer 
Support Material 

[0]

Defines the comparison test for convergence of a series.
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Integral Test

The integral test, pseries (Calculus) 
Computer 
Support Material 

[0]

Definition of the integral test and the pseries test.
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Integral Test Estimate

The integral test, pseries (Calculus) 
Computer 
Support Material 

[0]

A theorem about using integrals to estimate the difference between the limit of a series and one of its partial sums.
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Limit Comparison Test

Polynomial Approxs. and Series (Calculus) 
Computer 
Support Material 

[1]

Defines the Limit Comparison Test, which compares the ratios of terms in different sequences.
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Ratio Test

Ratio test (Calculus) 
Computer 
Support Material 

[0]

Defines the Ratio Test for convergence of an infinite series.
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Series and Convergence

Concept of infinite series (Calculus) 
Computer 
Support Material 

[0]

An introduction to series and rules for their convergence.
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Limit Comparison Test

Comparison test (Calculus) 

Tool 

[0]

Uses the Limit Comparison Test to determine whether the sum from 1 to infinity of 5^n/(7^nn) converges.
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The Average Approximating Met...

Polynomial Approxs. and Series (Calculus)+ 
Computer 
Tool 

[1]

The average approximating method on the functional adjustment quantity (Sokolov's method makes increasing for the rate of convergence of series solution of the Volterra integral equation. ...
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Absolute Convergence

Polynomial Approxs. and Series (Calculus) 
Flash 
Tool 

[0]

Discusses the absolute convergence test for infinite series.
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Absolute Convergence

Polynomial Approxs. and Series (Calculus) 
Flash 
Tool 

[0]

Uses absolute convergence to determine whether the sum from 2 to infinity of cos(n)/(1n^3) converges.
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Absolute Convergence

Polynomial Approxs. and Series (Calculus) 
Flash 
Tool 

[0]

Uses absolute convergence to determine whether the sum from 1 to infinity of sin((1)^n/n^2) converges.
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Comparison Test

Comparison test (Calculus) 
Flash 
Tool 

[0]

Uses the comparison test to find whether or not the sum from one to infinity of 1/(n^3+4n^2+5) converges.
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Comparison Test

Comparison test (Calculus) 
Flash 
Tool 

[0]

Uses the comparison test to find whether or not the sum from one to infinity of 1/(n^34n^2+5) converges.
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Comparison Test

Comparison test (Calculus) 
Flash 
Tool 

[0]

Uses the comparison test to find whether or not the sum from one to infinity of n/(n^35) converges.
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Comparison Test

Comparison test (Calculus) 
Flash 
Tool 

[0]

Uses the comparison test to find whether or not the sum from one to infinity of 5^n/(7^n+1) converges.
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Comparison Test

Comparison test (Calculus) 
Flash 
Tool 

[0]

Discusses the mathematical basis of the comparison test.
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Comparison Test

Comparison test (Calculus) 
Flash 
Tool 

[0]

Uses the comparison test to find whether or not the sum from one to infinity of n/(n^3+1) converges.
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Integral Test

The integral test, pseries (Calculus) 
Flash 
Tool 

[0]

Discusses the integral test by comparing integrals and partial sums.
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Integral Test

The integral test, pseries (Calculus) 
Flash 
Tool 

[0]

Uses the integral test to determine whether the sum from n=1 to infinity of n/(n^2 +7) converges.
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Integral Test

The integral test, pseries (Calculus) 
Flash 
Tool 

[0]

Uses the integral test to determine whether the sum from n=1 to infinity of n/(n^2 +7)^3 converges.
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