We have the sequence . To find the lower bound define . A little work shows that and the the second derivative is positive at that value, therefore it is an relative minimum. So now checking 0 the left-endpoint of the domain we find that is a lower bound. Now we can show that is unbounded above, the reason being that for every you can find a number such that . Also you can note that as n gets arbitrarily large that which clearly is unbounded above.