this is far as i got.. how can i finish this?
i m having a problem with that n!
You made a slight error. It should be $\displaystyle \lim_{n\to\infty}\left|n(2x-1)\right|$. Now this is obviously not less than one except for the value of x such that $\displaystyle 2x-1=0$. You could also notice in the beginning that the factorial will dominate the exponential regardless of the base and cause $\displaystyle \lim_{n\to\infty}n!(2x-1)^n$ to diverge to infinity for any value of x.