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Geometric series

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Useful for: MCR3U IB Math AA SL & HL IB Math AI SL & HL

Learn it The sum of the first n terms of a geometric series is Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1.

Example: A phone tree: 1 person calls 3, each calls 3 more… How many people are called in 6 rounds?

  1. 3 + 9 + 27 + … for 6 terms: a = 3, r = 3.
  2. S = 3(3⁶ − 1)/(3 − 1) = 1092 people.

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