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Alternating Series Exploration

Alternating Series Exploration
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2019-08-14 09:45
SequenceCalculusGraphing
This example demonstrates the convergence and sum of an alternating series through dynamic visuals, showing how partial sums approach a limit. Key math concepts include sequences, series, limits, function approximation, and geometric intuition. It uses GeoGebra commands like Sequence, Sum, and Slider to generate and accumulate series terms. Suitable for high school and above students to understand series theory and applications.

GeoGebra Commands & Parameters

  1. Sequence(1, n, 1) → L_1
  2. Sequence(((-1)^(i + 1) * 2 / i^(2)), i, 1, n) → L_2
  3. Sequence((i, Sum[L_2, i]), i, 1, n) → L_3
  4. Sum(L_2, n) → a
  5. Sequence(((-1)^(i + 1) * 2 / i), i, 1, n) → L_4
  6. Sequence((i, Sum[L_4, i]), i, 1, n) → L_5
  7. Sum(L_4, n) → b
  8. Sequence(((-1)^(i + 1) * ((2 * i) + 3) / (i + 1)), i, 1, n) → L_6
  9. Sequence((i, Sum[L_6, i]), i, 1, n) → L_7
  10. Sum(L_6, n) → c