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

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 )