All Questions

Is there any closed form expression for the following serie? $$\sum_{k=2}^\infty(-1)^k \left(- \frac{1}{2}\right)^{\frac{k(k+1)}{2}}$$ Or at least a proof that it is an irrational number. The ...

I've asked this question on MSE but I didn't get a convincive answer so I'm trying here. Here is the question : Let $\sigma:\mathbb{N}\longrightarrow\mathbb{N}$ be strictly increasing, and consider ...

One of the ways of accelerating the convergence of a series is by transforming into a faster series using optimal parameters. Examples of this approach can be found in this paper. I obtained a ...