N'th power inequality
Posted: Sat Apr 06, 2013 12:52 am
All $a_{i}$ are positive real numbers.Prove that,
\[\sum_{cyclic} \frac{1}{a_{i}^{n}+a_{i+1}^{n}+......................+a_{i+n-2}^{n}+a_{1}a_{2}.....a_{n}} \leq \frac{1}{a_{1}a_{2}..........a_{n}}\]
\[\sum_{cyclic} \frac{1}{a_{i}^{n}+a_{i+1}^{n}+......................+a_{i+n-2}^{n}+a_{1}a_{2}.....a_{n}} \leq \frac{1}{a_{1}a_{2}..........a_{n}}\]