# Browse Classroom Capsules and Notes

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Displaying 101 - 110 of 1214

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

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.