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This is a standard trick that you’ve probably seen before. S n = a+ ar+ ar2 + :::+ arn rS n = ar+ ar2 + :::+ arn +arn+1 1. 7 TAYLOR AND LAURENT SERIES 2 When we subtract these two equations most terms cancel and we get S n rS n= a arn+1 Some simple algebra now gives us the formula in Equation 1. De nition. Anin nite geometric serieshas the same form as the nite geometric series except there ...
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