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Infinite geometric series

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Useful for: IB Math AA SL & HL AP® Precalculus

Learn it If −1 < r < 1, the terms shrink toward 0 and the series has a finite sum: S∞ = a/(1 − r). If |r| ≥ 1 the series has no sum.

Example: A ball dropped from 10 m bounces back to 60% each time. Total distance travelled?

  1. Down: 10. Then up-and-down pairs: 2 × (6 + 3.6 + …) = 2 × 6/(1 − 0.6) = 30.
  2. Total 40 m.

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