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Timmy is tired. He does not want to add the infinite terms of . So instead, he just adds the first three terms.

  1. How far is his result from the actual sum of the infinite series? (This is called his “error.”)

    For an infinite geometric series:

  2. What would his error have been if he added the first four terms?

  3. Generalize his error. That is, if he adds up terms of this geometric series, what will his error be?

    For a finite geometric series:

    Substitute and into the formulas in the hints then evaluate.