Notice that the denominator is a geometric sequence. What do we know about the sum of a geometric sequence?
See this elegant answer # 11 by Max Wong: https://web2.0calc.com/questions/help-plzzzz_3
I wouldn't think of it as "elegant," but it's a really interesting approach to the problem.
Whoa, no need to get belligerent like that. I was just pointing out that I don't really consider that solution elegant, and that's my opinion. I think that it's possible to do it faster if you know the formula for the sum of a geometric series.
I agree that guest did sound abrupt, however, you made a statement and guest asked you to put your typing fingers where your mouth was.
It is reasonably obvious that you do not know how to answer the question yourself so you were not in a position to judge if Max's answer was elegant or not.
I think Max's answer was very impressive.