You can prove by induction as before. We have;
First we shall prove that is true then that is true. Let ;
and thus is true. Now assume is indded true and hence
Since and we can multiply the side of the inequality by and the by and not change the inequality hence,
Thus is true. Since this is the case and is true then we can conclude that is true and .
Alternatively we could prove this directly. We know that and thus it follows that and hence,
which is negative iff provided that which is given in this case.
Hope this helps.