Does anyone have any knowledge on these? I look at an example of a direct or limit comparison and i see what they are doing, but I have no idea how they got the "comprable" term.... for example the sum (n = 1) to infinity n/(n^2 +1) you can use either test, but how do you choose what to compare it to? this is my issue and it occurs on other problems where you have to use comparison... I know for direct comparison you need to compare the original sum to something smaller or larger than itself and depending on what it does will tell you if it converges or diverges. I know this, but I do not know what to compare it to!! Do you just pick something out of thin air that is in the same general form as the sum and make it smaller or larger? aaaarrrghhhhh!!!!!