Test the series below for convergence using the Root Test.

$\displaystyle {\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}^{{{2}{n}}}}$

The limit of the root test simplifies to $\displaystyle \lim_{{{n}\rightarrow\infty}}{\left|{f{{\left({n}\right)}}}\right|}$ where

$\displaystyle {f{{\left({n}\right)}}}=$ Preview Question 6 Part 1 of 3  

The limit is: Preview Question 6 Part 2 of 3  
(enter oo for infinity if needed)

Based on this, the series