Limit proof on Sequence Convergence

  • Thread starter Bipolarity
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  • #1
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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
 

Answers and Replies

  • #2
22,129
3,297
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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