# find the radius of convergence of the power series $\sum _1^{\infty} n^{-\sqrt n} z^n$

find the radius of convergence of the power series $\sum _1^{\infty} n^{-\sqrt n} z^n$

here $a_n= n^{-\sqrt n}\\$

$\frac{1}{R}=\lim_{n \rightarrow \infty} [ n^{-\sqrt n} ]^\frac{1}{n}$ for further i didnt get any one can help

Hint: $$(n^{-\sqrt{n}})^{1/n}=n^{-1/\sqrt{n}}=e^{\frac{-\log n}{\sqrt{n}}}$$
• $a=e^{\log a}$ the apply the property $\log(a^b)=b\log a$ – b00n heT Sep 7 '16 at 8:21