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3 questions with no upvoted or accepted answers
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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 ...
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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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Sum power series not continuous unit circle
This is (probably) not a research question and I already asked it on StackExchange but I got no answer over there.
Let us consider the sequence $(a_n)_{\geq 1} = \left(\frac{\cos(2\sqrt{2n}+\frac{\pi}{...
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