We study the convergence sets of a class of alternating series. Among other things, our results establish the convergence of the series $\sum_n (-1)^n|\sin n|/n$.
Irrationality and Transcendence of Alternating Series Via Continued Fractions
A new construction of the real numbers by alternating series
The convergence of an alternating series of Erdős, assuming the Hardy--Littlewood prime tuples conjecture
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