Another inequality with powers: The proof for previous inequality does not trivially extend, I guess.
$$\text{For}\; n>2,\quad\quad(2n)^{n-1}> 1^{n-1}+3^{n-1}+...+\left( 2n-3\right) ^{n-1}+\left( 2n-1\right) ^{n-1}$$
Another inequality with powers: The proof for previous inequality does not trivially extend, I guess.
$$\text{For}\; n>2,\quad\quad(2n)^{n-1}> 1^{n-1}+3^{n-1}+...+\left( 2n-3\right) ^{n-1}+\left( 2n-1\right) ^{n-1}$$