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The value of the series  is a real number greater than 8. Find all possible values of x, giving your answer in interval notation.

 Feb 22, 2019
 #1
avatar+100570 
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The common difference, r, = x

 

So...using the formula fot the sum of an ifinite geomertic series, we have

 

4 / { 1 - x) > 8    

 

1 /(1 - x) > 2

 

1 > 2 ( 1 - x)

 

1 > 2 - 2x

 

2x > 1  

 

x > 1/2

 

However....x  must also be < 1

 

So....

 

1/2 < x < 1  or   ( 1/2, 1 )

 

cool cool cool

 Feb 22, 2019

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