# Browse Classroom Capsules and Notes

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Displaying 1031 - 1040 of 1212

The author characterizes the set of possible limits of subsequences of a given sequence.

Two visual proofs of some exponential inequalities are presented.

Given any positive integer $n$, find polynomial curves that have exactly $n$ tangent lines which intersect the curve exactly once.

Solving Pell Equations using Fibonacci-like sequences

In the game of tennis, if the probability that player $A$ wins a point against player $B$ is a constant value $p$, then the probability that $A$ will win a game from deuce is \(p^2/(1 - 2p...

Solving an expected value problem without using geometric series

Another approach to trisecting any acute angle

Characterize positive integers which can be written as a sum of consecutive integers

Generalized examples of a sphere and a circumscribing cylinder, which can also be used to calculate the surface area of a sphere.

Describing Pythagorean Triples with one square side and a triangular side. Their number is infinite.