So basically i have to prove that for $A = \lim_{n\to \infty}inf\sqrt[n]{|a_n|}$ that if $A>1$ the serie $\sum_{i=1}^\infty a_n$ diverges. So for $ε=k - A$ and $A>1$ $A = \lim_{n\to \infty}\sqrt[n]{|a_n|}$ that means that there is afinite amount of terms of $\sqrt[n]{|a_n|}$ under $k = A - ε$ So there is a real number $n_0< n$ so that $\sqrt[n]{|a_n|} > k$
I really dont know where im going with this what is next or have i started completely on the wrong foot.