Well if you do the limit comparison you will need to calculate the limit
This is an indeterminate form of infinity times zero. What methods have you learned to resolve these types of limits? The only other method I can think of is to use a Taylor series expansion, but that is usually covered after the topics you are learning right now.
Here is a link to the theorem:
L'Hôpital's rule - Wikipedia, the free encyclopedia
This is of the form zero over zero so we take the derivative of the numerator and denominator to get