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Geometric Series​​​​

Source: Ball - fdmsd8yea/iStock/Getty Images

A Computer Virus

A computer virus can be spread computer to computer.

Source: Computer Virus - bagotaj/iStock/Getty Images

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Lesson Goals

  • Define a geometric series.
  • Derive a formula for the sum of the first \(n\) terms in a geometric series (\(S_n\)) and use this formula to calculate sums of given geometric series.
  • Solve problems involving the application of geometric series.

Try This

A computer virus infects two computers in its first iteration. In each subsequent iteration, the previously infected computers infect three more computers.

A computer virus infecting two computers at first and spreading to other computers with each iteration.

Source: Computer Virus - bagotaj/iStock/Getty Images

After the \(20\)th iteration, how many computers have been infected in total?