Given that ${\displaystyle \underset{n=0}{\overset{}{}}}{a}_n$ is convergent. Select all the True statements below:

A$.\underset{n}{lim}{a}_n=0$

B$.{\displaystyle \underset{n=1}{\overset{}{}}}\frac{a_n}{n}$ is convergent.

C

D$.\underset{n}{lim}|\frac{a_{n+1}}{a_n}|1.$

E$.{\displaystyle \underset{n=1}{\overset{}{}}}n-a_n$ is convergent.