Motivated by a proof without words for the sum of the alternating harmonic series, this article delves into some interesting questions regarding a series to which the usual convergence tests do not ...

Do examples as in the title exist? It depends on how the term Riemann sum is understood. For the standard, left, or right Riemann sums such examples do not exist. However, as we will see, they do ...

The Riemann Hypothesis, a central unsolved problem in mathematics, posits that all non-trivial zeros of the Riemann zeta function lie on the critical line in the complex plane. This conjecture is not ...

Integrable systems and differential equations underpin a vast area of contemporary mathematical physics, where the synthesis of analytical techniques and geometric insight yields exact solutions to ...