Have you tried with induction? (Maybe that will work)
I have become interested in this problem and have spent a great deal of time trying to get induction (among other things) to work, but have not been successful. Hopefully, someone can show me where I am going wrong. Obviously the statement is true for the base case of n = 1. So I stated the induction hypothesis :
Assuming this is true, I then added to get:
I can't figure out how to get rid of the in the numerator of the integrand.
edit: sorry about my edits...this board has some unexpected idiosyncrasies concerning the
\left and \right operators in ...
I should add that this problem has also been posted on the forum which I help moderate, and I have posted the same problem I have in using induction.
The OP is an infrequent visitor there, and it may be a while before we hear from them to get any feedback on the context of the problem.