Question A series is what happens when you keep adding terms forever: Σ aₙ. But "add forever" is not a casual instruction — it is a claim about the sequence of partial sums sₙ = a₁ + … + aₙ. If those running totals approach a finite limit S, the series converges to S. If the totals wander or explode, the series diverges.
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Define series convergence via the sequence of partial sums Compute or interpret partial sums, including telescoping patterns Apply the necessary condition aₙ → 0 Reject the false claim that aₙ → 0 implies convergence
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Series Σ aₙ ↔ sequence of partial sums sₙ Rain gauge: does the running total settle?
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