Question When signs flip + β + β, cancellation can rescue a series that would otherwise diverge. Alternating series ask: can those cancellations save a barely dying positive skeleton? Absolute convergence β Ξ£ |aβ| converges β is the strong form. Conditional convergence means the signed series converges but the absolute version does not. They are not the same idea wearing different clothes.
Consider
Apply the alternating series test (AST) checklist Estimate the remainder by the next term Distinguish absolute and conditional convergence Reject 'alternating β converges' and 'conditional = absolute'
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Signs flip: can cancellation save a slow series? Absolute vs conditional β not the same
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