# Lim sup an /bn = lim sup an / lim sup bn?

hello,
2 technicality questions:

1) lim sup an /bn = lim sup an / lim sup bn?
2) if lim sup an /bn is finite does that mean
that the sequence {an/bn} bounded?

thank you.

1) no. Take (an)=(0,1,0,1,0,1,...) and (bn)=(1,-1,1,-1,1,-1,...).
2) I believe that this is true...

mathman
2) is false. Let bn=0 for a finite number of n's.

Uh, if a bn=0, then the sequence $$a_n/b_n$$ isn't even good defined. I didnt think the OP meant that...

yes ofcourse, i meant bn strictly positive.
ok, thanks a lot

George Jones
Staff Emeritus