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Browse Classroom Capsules and Notes

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Displaying 151 - 160 of 1211

Infinite series representing several functions, and several series representing \(\pi\) are derived using tabular integration by parts.

The author discusses an intuitive direct proof of the fact that functions with zero derivative must be constant, which turns into a rigorous proof by simply invoking the completeness of the...

Various examples of convergent Newton sequences which do not converge to a zero of the underlying function are given.

A short proof of the well-known fact that the unit interval \([0,1]\) is uncountable is presented by means of a simple infinite game. The author also used this game to show that a (non-empty)...

A solution to a probabilistic Putnam Exam Problem is presented.

Primality testing via repeated differentiation of certain functions is the topic of this paper.
The author discusses the distribution of solutions to a polynomial congruence as the modulus varies.

The author discusses the question of when to add milk to coffee in order to maximize cooling.

A Fundamental-like Theorem of Algebra for exponential functions is discussed and proved.

Hansheng Yang and Heng Yang used the arithmetic-geometric mean inequality to prove that the sequence \([1+1/n]^n\) is monotonic increasing converging to \(e\) whereas \([1+1/n]^{n+1}\) is...