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Alternating Series

Sign flips, conditional convergence, and remainders · BC Calculus · greeting

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Owl · Mock interview — Alternating Series. I ask; you answer.

Owl · We'll run the alternating series test checklist, estimate remainders, and build examples that separate absolute from conditional. Two traps to dodge: "alternating always converges," and "conditional equals absolute."

Larry’s gold answer — Show text to read it out loud.

Larry · gold answer · For Σ (−1)^{n+1}/n, the magnitudes 1/n decrease to 0, so AST should say it converges — even though the harmonic series diverges.

Owl: We'll run the alternating series test checklist, estimate remainders, and build examples that separate absolute from conditional. Two traps to dodge: "alternating always converges," and "conditional equals absolute."

You: —