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Full-Text Articles in Mathematics
The Last Digits Of Infinity (On Tetrations Under Modular Rings), William Stowe
The Last Digits Of Infinity (On Tetrations Under Modular Rings), William Stowe
Celebration of Learning
A tetration is defined as repeated exponentiation. As an example, 2 tetrated 4 times is 2^(2^(2^2)) = 2^16. Tetrated numbers grow rapidly; however, we will see that when tetrating where computations are performed mod n for some positive integer n, there is convergent behavior. We will show that, in general, this convergent behavior will always show up.
On The Sum Of The Reciprocals Of Squares, Hussam Ibrahim
On The Sum Of The Reciprocals Of Squares, Hussam Ibrahim
Celebration of Learning
The Fourier Series has always been a great tool by turning the most complicated functions into a simple approximation by several sine and cosine terms. However, given the fact that its called an approximation arouses the question of how accurate is this approximation, especially with functions that have a corner at x values. In this project, we will show how the series that is the sum of the reciprocals of squares arises in the study of Fourier series. We will discuss the convergence and the rate of convergence of this series. This result arose during exploration on mathematical software Sage. …