Give an example of an unbounded sequence that does not diverge to positive infinity or to negative infinity. Solution et [s_n=n] if [n] is even and 0 if [n] is odd, so the sequence is 0,2,0,4,0,6,... This is unbounded but doesn\'t diverge to infinity or negative infinity because there will always be values for which [s_n=0] no matter how large [n] is..