Limit Comparison Test for Series

[mohabitar]

Just a general question, but I find it hard to come up with a b[n] to compare to a[n]. When the book does it, they come up with stuff to compare to a[n] that I would have never thought of. Is there any criteria, things to look for, etc., for coming up with a b[n] to compare to a[n]?

 

[fzero]

Obviously you need to use b_n for which you already know the convergence. You also want to pick b_n for which the limit of a_n/b_n is convenient and within the criteria of the comparison test.