the dividing of a_n+1 /a_n is not conlusive
?
Now, you have me confused! is the same as and that is the definition of "decreasing".
Or are you saying that you know you have to prove one of those but don't know how?
I would look at .
Now, in the limit, as k goes to infinity, that fraction goes to 1 so this "eventually" decreases to 0.
If you really need to prove that it is decreasing for all k greater than or equal to 1, I recommend Plato's suggestion. Take the dervative of .