- #1

- 1

- 0

## Homework Statement

Show that [tex]\left( 1 - \frac{\ln n}{kn} \right)^n > \frac{1}{n^{1/k} + 1}[/tex] holds for all integers [tex]n\geq 1[/tex] and [tex]k\geq 2[/tex].

## The Attempt at a Solution

I first tried to find a proof for [tex]k=2[/tex] by showing that the quotient LHS/RHS goes to 1 and has negative slope everywhere, but this becomes rather unwieldy.