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Geometric Series - Problem 5

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Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

If you imagine adding together squares that get smaller and smaller in size, then you can imagine how this visual representation of a sum would approach a fixed total area. This is what is meant by the idea of convergence, and we can find such an infinite geometric series, or sum, using a simple formula. In contrast, if you imagine adding squares that get bigger and bigger in size, then you can imagine that idea of divergence. We can find a geometric, infinite sum if and only if the absolute value of the common ratio, r, between successive terms is less than one and greater than zero.

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