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Limit proof on Sequence Convergence

  1. Apr 29, 2012 #1
    Consider a sequence [itex] \{ a_{n} \} [/itex].

    If [tex] \lim_{n→∞}a_{n} = L[/tex] Prove that [tex] \lim_{n→∞}a_{n-1} = L [/tex]

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



    BiP
     
  2. jcsd
  3. Apr 29, 2012 #2
    Start by writing the definitions of

    [tex]\lim_{n\rightarrow +\infty}{a_n}=L[/tex]

    and

    [tex]\lim_{n\rightarrow +\infty}{a_{n-1}}=L[/tex]
     
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