/sci/ - Science & Math

Can someone help explain the thought process behind this question?
So I had completely guessed this questions answer by accident so I don't really understand it.
Looking at the answer, how did the person come to know that he should compare it to (1/2n)? Personally, I would've never thought of that or any of the other comparisons used in other sites such as (1/n - 1/2n) so I would definitely get this question wrong if I were to get it on an exam.