Csdrhrt

2 $begingroup$ I'm having trouble seeing when to use the root test. nth powers occur, but I think the ratio test is easier: Here is the problem: $$sum_{n=1}^{infty} frac{x^n}{n^44^n}$$ So the ratio test seems to work here, but can't the root test be used to? The problem is that the $n^4$ doesnt play well with the root test right? Here is the beginning of my solution with the ratio test: $$biggr lbrack frac{a_{n+1}}{a_n} biggr rbrack = biggr lbrack frac{x^{n+1}}{(n+1)^4 * 4^{n+1}} * frac{n^4*4^n}{x^n} biggr rbrack = biggr lbrack frac{x*n^4}{(n+1)^4 * 4} biggr rbrack = frac{x}{4}$$ So I don't think the explanation for when to use the root test is totally right right? I can't really use it here because the $n^4$ causes some problems with the root test right?