# Browse Classroom Capsules and Notes

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Displaying 111 - 120 of 1211

How do sequences of the form $(1+x/n)^{n+\alpha}$ with $x >0$ approach their limits?

A combinatorial proof of a formula for the sum in the title is provided.

Two visual proofs of some exponential inequalities are presented.

The limit of the ratio of the geometric mean to the arithmetic mean of certain sequences is studied, using Riemann sums.

The author offers two examples that illustrate important central ideas in introductory linear algebra (independent or dependent vectors; invertible or singular matrices) which may aid students in...

A row (column) of a matrix is called “extraneous” if it is a linear combination of the other rows (columns).  The author shows that deleting an extraneous row or column of a...

A number game and the discussion of probabilities of winning

A new approach to finding the center of gravity for quadrilaterals

In this note the convergence of certain modified $p$ -series is discussed.

A family of curves whose lengths are closely related to Pythagorean Triples and therefore rational