Repeating Decimals As An Infinite Series
Repeating decimals can also be expressed as an infinite series. That is, repeating decimals can be shown to be a sum of a sequence of numbers. To take the simplest example,
The above series is a geometric series with the first term as 1/10 and the common factor 1/10. Because the absolute value of the common factor is less than 1, we can say that the geometric series converges and find the exact value in the form of a fraction by using the following formula where a is the first term of the series and r is the common factor.
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“I have met few men in my life, worth repeating eight times.”
—Elizabeth Cady Stanton (1815–1902)
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