The sum of an infinite geometric series is $27$ times the series that results if the first three terms of the original series ar
e removed. What is the value of the series' common ratio
1 answer:
Let
be the first term in the series and
the common ratio. Then the infinite series converges to

Removing the first three terms from the left side effectively multiplies the right side by 27, so

By elimination,

Solve for
. We can eliminate
so that

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