Does the Series (n^4+1)^(1/2)/(n^3+n^2) Converge or Diverge?; Using the Limit Comparison Test

This series looks tricky. It is the perfect type of function to use the limit comparison test on however. First, we must find the dominant terms of the numerator and denominator; that is to say that we must find a simpler function that behaves like our function and that we know converges or diverges and that will make the limit of the fraction of the functions easy to evaluate at infinity. For this, the function 1/n is sufficient. It behaves in the same way and we know it diverges. Since the resulting limit is greater than 0 and is finite, the original function is also divergent.