convergent or divergent?

[hgaon001]

-The sum from n=1 to infinity of (5)/4throot[(n^3)+4n+1]

and..

-The sum from n=1 to infinity of (2n)/4throot[(n^8)+(2n^4)+1

 

[pka]

Both of the problems are ‘made’ for the use of the limit comparison test.
In the first, compare with \(\displaystyle \[\frac{1}{{\sqrt[4]{{n^3 }}}}\).

In the second, compare with \(\displaystyle \[\frac{1}{n}}\).