(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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].

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proving an inequality involving exponentiation

**Physics Forums | Science Articles, Homework Help, Discussion**