$$\sum_{n=0}^\infty n!x^{n^2}$$   Can anyone tell me what will be the radius of convergence for this power series. According to me it is $0$.   If you can please show me how to go about it if I am wrong.
The question is to calculate the radius of convergence of $\sum\limits_{n=0}^\infty n!x^{n^2}$.  I dont know how to calculate R.O.C for such type of questions involving $n^2$ as power of x. How do we do this? Any help appreciated.
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