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Infinite Series

Partial sums and when the running total settles · BC Calculus · greeting

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

Owl · We'll build partial-sum tables, peek at telescoping cancellation, and meet the necessary test: if aₙ doesn't go to zero, the series cannot converge — and the converse trap that fools almost everyone.

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

Larry · gold answer · So the series converges only when the partial sums sₙ converge as a sequence. The infinite sum is really lim sₙ.

Owl: We'll build partial-sum tables, peek at telescoping cancellation, and meet the necessary test: if aₙ doesn't go to zero, the series cannot converge — and the converse trap that fools almost everyone.

You: —