I'm asked to prove that if $u_{n+1}-u_n=o\left(1\right)$ then $\displaystyle \frac{u_n}{n}\underset{n \rightarrow +\infty}{\rightarrow}0$.
I know that I can write that for all $\epsilon>0$, it exists $N$ such that if $n \geq N$ then $\left|u_{n+1}-u_n\right|<\epsilon'$. I'v tried to choose $\epsilon'=n\epsilon$ then I have $$\left|\frac{u_{n+1}}{n}-\frac{u_n}{n}\right|<\epsilon$$
But I cannot conclude, any hint ?