I am working on the following power series. (Cant copy images yet)
I have applied the ratio test on the series ignoring the $-ln(2)$, and have reduced it down to
When i take the limit of this i end up with $x/2$. I know the interval of convergence is abs$(x) < 2$.
Do i need to include the $-ln(2)$ in this part, or have i done something wrong in the calculation, as $x/2$ doesnt seem to be right. Also, does the $-ln(2)$ affect the actual values of the interval and radius of convergence.
I also concluded it was absolutely convergent for all values, and conditionally convergent for none. Is this correct?