Determine the radius of convergence of two power series:
1) $\dfrac{x^{6n+2}}{(1+\frac{1}{n})^{n^2}}$
2) $\displaystyle\sum_{n=0}^{\infty}a_n(x-2017)^n$, where $a_n=\dfrac{1}{2}$ if $n$ is even and $a_n=\dfrac{1}{3}$ if $n$ is odd.
In both problems, I use root test and got the answer for (1) is $e^{1/6}$ and for (2) is $1.$ Are the answers are correct?