Homework Statement
Show that \left( 1 - \frac{\ln n}{kn} \right)^n > \frac{1}{n^{1/k} + 1} holds for all integers n\geq 1 and k\geq 2.
The Attempt at a Solution
I first tried to find a proof for k=2 by showing that the quotient LHS/RHS goes to 1 and has negative slope everywhere, but...