I have an exercise that states:
Suppose that $f:\mathbb{N}\rightarrow\mathbb{R}$. If $\lim_{n\rightarrow\infty}f(n+1)-f(n)=L$, prove that $\lim_{n\rightarrow\infty}f(n)/n$ exists and equals $L$.
I have wracked my brain over this exercise for about 5 hours now and really have not gotten ANYWHERE with it...does anyone have a suggestion on how begin proving this?
Thank you.