You are here

Home » Programs » Faculty and Departments » Browse Classroom Capsules and Notes

Browse Classroom Capsules and Notes

You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.

Displaying 21 - 30 of 67

The \(n\)th Derivative Test and Taylor Polynomials Crossing Graphs

The author describes \(n\)th derivative test, a generalization of 2nd derivative test, then applies it to give a quick proof of a condition for determining when the graph of a...

Convergence-Divergence of \( p\) -Series

This article is a discussion of convergence and divergence of \(p\)-series without using the Integral Test.

Investigating Possible Boundaries Between Convergence and Divergence

Once students master the Integral Test, it is useful to show that there cannot be a series on the boundary between convergence and divergence.

An Improved Remainder Estimate for Use with the Integral Test
If a series is shown convergent by the integral test, get a sharper than usual estimate for the error.
A Novel Approach to Geometric Series

A novel way of deriving the sum of a geometric series from a financial situation

A Visual Approach to Geometric Series

Physical properties of a book are used to illustrate convergence.

Introducing the Sums of Powers

This is an attempt to motivate as well as prove formulae for sums of powers of integers.

An Elementary Proof of Monotonicity

Easily followed algebra is used to show that two familiar bounding sequences converge to \(e\).

Another Proof for the \( p\) -Series Test

Convergence of the \(p\)-series is analyzed by considering partial sums.

A Sequence Related to the Harmonic Series

Links the number e to properties of a sequence related to the harmonic series

Pages