Identify the smallest in relation to so that the proposition can be proved using mathematical induction (over n).

Fiddling around with the numbers is a least condition for the inequality, but how can I find out the relationship between k and n for all n?

Just as a beginning:

hypothesis:

re-write the hypothesis:

for :

but from this we see that:

Is it possible to conclude that:

which is just nonsense. I think? Can someone please help?!