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Find all r for which the infinite geometric series \(2 + 6r + 18r^2 + 54r^3 + \dotsb.\) is defined. Enter all possible values of r, as an interval.

 Apr 20, 2020
 #1
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Since we have a geometric series, the possible values of r are in the interval (-1,1).

 Apr 20, 2020
 #2
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Are you sure? I entered in that answer and it was wrong.

qwertyzz  Apr 20, 2020
 #3
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Since each term is  3r  times the preceding term, this will be a geometric series for whatever number you choose for r.

Interval form:  (-infinity, infinity).

 Apr 20, 2020
 #4
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I entered that in and it didn't work,  Can you check again?

qwertyzz  Apr 20, 2020
 #5
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Common ratio is 3r

For the geometric series to converge, the absolute value of the common ratio has to be less than 1

|Common ratio| < 1
|3r| < 1
-1/3 < r < 1/3
or

(-1/3,1/3)

 Apr 20, 2020

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