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Geometric Series - Problem 5


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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