Does the Limit Comparison Test Require an to Be Greater Than bn?

[member 508213]

In my textbook it says if you are comparing limn->infinity of an/bn an>0 and bn>0 for the limit comparison test to apply.

It says nothing about "an" having to be greater than "bn", so as long as both are positive for each term I can use the limit comparison test right? It isn't like the direct comparison test where you need to worry about having all of a sequence's terms be larger/smaller than the one you are comparing to?

Thanks

 

[mathman]

If an/bn -> 0, you know very little about bn if you are using an as a comparison.

 

[vela]

In my textbook it says if you are comparing limn->infinity of an/bn an>0 and bn>0 for the limit comparison test to apply.

It says nothing about "an" having to be greater than "bn", so as long as both are positive for each term I can use the limit comparison test right? It isn't like the direct comparison test where you need to worry about having all of a sequence's terms be larger/smaller than the one you are comparing to?

Thanks

Right. The limit comparison test tells you if the two sequences have the same sort of behavior when n gets large. You don't need one sequence to be greater than or less than the other to see if they behave similarly for large n.