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3 questions
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Limit of lacunar power series at $1^-$
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 ...
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Convergence acceleration of a series by using optimal parameters
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 ...
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Is there any closed form expression for $\sum_{k=2}^\infty(-1)^k \left(- \frac{1}{2}\right)^{\frac{k(k+1)}{2}}$?
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 ...
