Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 6.3 National olympiad Prove it

Example 7.8 For non-negative real numbers $a, b, c, a+b+c=3$ , prove: for any $k \geqslant 0$ , we have
$a^{k} b+b^{k} c+c^{k} a \leqslant \max \left\{3, \frac{3^{k+1} k^{k}}{(k+1)^{k+1}}\right\}$

Solution

None

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