77-82 ■ Repeated Decimal Express the repeating decimal as a fraction.
The repeating decimal of as a fraction.
If , then the infinite geometric series converges.
The sum of the infinite geometric series, when it is convergent is given as,
Here, is the sum of infinite geometric series, is the first term of the sequence and is the common ratio of the sequence.
If , then the infinite geometric series diverges.
The repeating decimal can be written as a series,
Since the first term of the sequence is and the common ratio is
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