How do I show that the limit of (ln n)/(n^p) as n -> infinity, where p>0, converges to 0? I know that the denominator is the harmonic sequence (1/n^p) but I am not sure how to begin.
I think you can use l'Hopital's rule for $\displaystyle \frac{n^p}{a^n}$, but not $\displaystyle \frac{a^n}{n!}$. For the latter, my first thought would be mathematical induction.
You cannot use L'hospital's rule because the numerator and denominator are not equal to zero in the limit.
Also the function is not differentiable because it is only defined for n being natural number.
Is p a natural number? because it doesnt converge for 1>p>0