We can use the formula for the sum of a geometric series to quickly and accurately convert a repeating decimal into a ratio of integers, in other words, into a fraction with whole numbers in the numerator and denominator.
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Only if a geometric series converges will we be able to find its sum. The sum of a convergent geometric series is found using the values of ‘a’ and ‘r’ that come from the standard form of the series.
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Before we can learn how to determine the convergence or divergence of a geometric series, we have to define a geometric series. Once you determine that you’re working with a geometric series, you can use the geometric series test to determine the convergence or divergence of the series.
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