# Math Help - two tests covergence problem

1. ## two tests covergence problem

$\sum_{K=1}^{INFINITY}(\frac{k^{2}+1}{3k^{2}-2K+11})^{k}$
th a_k doesnt go to zero
so the series diverges
but by the n'th root test its coverges

where is my mistake
?

2. The limit of the general term IS zero...

3. then power of numerator and denominator ar equat
equal

so we get 1/3 in the infinity power=0

correct
?

thanks