Let . Prove that
I have proved for , but I'm stuck for n<0.
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Originally Posted by red_dog Let . Prove that
I have proved for , but I'm stuck for n<0. Just out of curiosity, how did you prove the result for . Did you use a concavity argument? If so, I think you can extend it to negative values.
Consider and apply Jensen's inequality.
Originally Posted by Krizalid Consider and apply Jensen's inequality. Isn't that like what I said about using the concavity?
Didn't see your post, sorry.
Actually, it's even easier, we can tackle this without Jensen.
We have hence
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