Can we say if an infinite alternate series sums to a rational number given some specific conditions? Assuming the series converges, is there any test to know if it sums to a rational value? I know there is a similar question mentioned in the comment that basically seems to suggest that this is still an open question in mathematics. However, the kind of infinite series I am talking about in here is alternate ones. In other words, if we add "alternating" characteristics to an infinite series, does the problem still remains open?
2026-04-03 23:04:06.1775257446
Is there any rule on the convergence of an infinite alternate series?
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