Screw you, Mr. Cauchy.

I've spent the last several hours working (and the last two days thinking) about how to make this dang sequence Cauchy and searching for the criteria for making a series likewise. The conclusion to which I have come is as follows: even if I cared why bounded sequences can be made Cauchy and even if I could fake my way through the proof of why Cauchy sequences are convergent, it wouldn't make me a better or more impressive human being and it certainly wouldn't make my school year or summer any less sweet. Why anyone would lock themselves in a room for years to figure this kind of stuff out in the first place is beyond me. Good-bye mathematicas.