1. The problem statement, all variables and given/known data Thm: If a sequence is Cauchy than that sequence is bounded. However Take the partial sums of the series (sigma,n->infinity)(1/n). The partial sums form a series which is Cauchy. But the series diverges so the sequence of partial sums is unbounded. Sequence of partial sums is Cauchy b/c d(1/x,1/(x+1))=1/(k(k+1)) -> 0 as k->infinity Have I done something wrong?