# Limit proof on Sequence Convergence

1. Apr 29, 2012

### 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

2. Apr 29, 2012

### micromass

Start by writing the definitions of

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

and

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