In this video, I go over an example of converting the number 2.3171717... (with infinite repeating 17) into a fraction by writing the repeating 17s as an infinite geometric series with common ratio 1/100, hence the sum is convergent. Thus, we can use the formula for the sum of a geometric series, and a bit of algebra, to obtain the fraction of integers 1147/495. This is a great example illustrating the powerful tool that the geometric series is in simplifying a number made up of repeating digits.
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