Find the maximum among $1,2 ^ { 1/2 } , 3 ^ { 1/3 } , 4 ^ { 1/4 } , \ldots$.
Maximum is $\sqrt [ 3 ] { 3 }$. Either check the maximum of the function $x ^ { \frac { 1 } { x } }$, or compare $\sqrt [ 3 ] { 3 }$ with $\sqrt [ n ] { n }$.
Find the maximum among $1,2 ^ { 1/2 } , 3 ^ { 1/3 } , 4 ^ { 1/4 } , \ldots$.