Limit proof on Sequence Convergence

[Bipolarity]

Consider a sequence \{ a_{n} \}.

If \lim_{n→∞}a_{n} = L Prove that \lim_{n→∞}a_{n-1} = L

I am trying to use the Cauchy definition of a limit, but don't know where to begin. Thanks.



BiP

 

[micromass]

Start by writing the definitions of

\lim_{n\rightarrow +\infty}{a_n}=L

and

\lim_{n\rightarrow +\infty}{a_{n-1}}=L