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The value of the series \(4+4x+4x^2+4x^3+\cdots\) is a real number greater than 8. Find all possible values of x, giving your answer in interval notation.

 Feb 20, 2019
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This is  a geometric series with a  common ratio of x

 

So we have that....using the sum of an infinite geometric series.....

 

4 / ( 1 - x) > 8

 

4 > 8 ( 1 - x)

 

4 > 8 - 8x

 

8x > 4

 

x > 1/2

 

However    x must also be < 1

 

So the solution is

 

(1/2 , 1 )

 

 

cool cool cool

 Feb 20, 2019
edited by CPhill  Feb 21, 2019

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