I was trying to prove that for arbitrary $A,B\in\mathbb{R}$ and any $p\in\mathbb{N}$ it holds
$(A+B)^p \leq 2^{p-1}(A^p+B^p)$
I'd appreciate some advice. Thanks a lot.
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Also: http://math.stackexchange.com/questions/722260/how-to-show-stp-le-2p-1sp-tp-for-p-gt1, http://math.stackexchange.com/questions/555002/proof-2n-1anbnabn. – Martin R Mar 06 '17 at 18:39
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It's wrong! Try $p=3$, $A=-2$ and $B=1$.
For $A\geq0$ and $B\geq0$ your inequality it's just Jensen for $f(x)=x^p$: $$\frac{A^p+B^p}{2}\geq\left(\frac{A+B}{2}\right)^p$$
Michael Rozenberg
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Oh, you're right. I was confused. Thank you very much for clearing that up. – Twexco Mar 10 '17 at 13:23
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