The Endless Bounce

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Drop balls with different bounce ratios r from a height h and watch the distance h + 2hr + 2hr² + ⋯ of an endlessly bouncing ball pile up as partial sum bars that approach the sum of the series h + 2hr/(1 − r). See that the sum grows as r nears 1, diverges when r = 1, and that the time until the ball stops is also finite, a geometric series with ratio √r.

Key conceptsgeometric series · sum of a series · partial sum · common ratio · convergence · divergence · series

• Calculus