According to the ratio test, a series is convergent when .
So get an expression for this limit, set it less than 1, then solve for x.
Not true at all. For any series, if you can show the series of absolute values is convergent, then so is the original series. What we are doing by taking the absolute value of the ratio in the ratio test is to check the convergence of the absolute value series. When this is convergent, so is the original series.