# 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...