*The author presents a visual proof of the closed form of a recursively defined sequence: \(a_2 = 3\) and \(a_n = 2 a_{n-1} + 1\)*

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 101 - 110 of 1212

*This article describes and encryption algorithm that can be used to transmit information between two parties such that each person can verify the other person's information.*

*This article uses a generalization of a three-way gunfight to motivate the construction and solution to a first order linear system of difference equations. The method of undetermined...*

*The author presents a visual proof of the formula for the sum of the first n consecutive products: \(1 \times 2 + 2 \times 3 + 3 \times 4 +\ldots + n \times (n+1)\).*

*How can we define multiplication of ordered pairs of real numbers to make \(R^2\) into a ring, or field? In this article, the author derives conditions for certain types of rings and extends...*

*The author proposes a visualization of the number \(e\) related to area of subsections of a ''tentagram''.*

*A generalization of the Mean Value Theorem for Integrals in terms of Riemann sums*

*A discussion of the overhand card shuffle using algebra*

*The author presents a visual proof of the formula for the sum of the first n consecutive products: \(1 \times 2 + 2 \times 3 + 3 \times 4 + ... + n \times (n+1)\).*

*The article describes how to find polynomials whose roots are given powers of the roots of an original polynomial.*