Determine the values of x for which this series.

Question

Determine the values of x for which the series converges (this is a geometric series.)

Answer 1

Because we know this is a geometric series, we know that the absolute value of the base must be less than 1. |5x-3.5|<1

-1 < 5x-3.5 < 1

2.5 < 5x < 4.5

0.5 < x < 0.9

So we know that it must be between 0.5 and 0.9. Since no other value is multiplied by this, we don't need to check endpoints (we'd typically do this if it were ratio/root test).