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kimmy0394
 2 years ago
Suppose {an} is a sequence that converges to a number
L > 0.
What is the limit of {an + 1}?
kimmy0394
 2 years ago
Suppose {an} is a sequence that converges to a number L > 0. What is the limit of {an + 1}?

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KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Since it converges, you have that for all \(\epsilon>0\), \(La_n<\epsilon\) for all \(n>N\) for some \(N\in\mathbb{N}\). Now, we guess that \(\{a_n+1\}\) converges to \(L+1\). Look at \(L+1(a_n+1)\). What can you say about it?

kimmy0394
 2 years ago
Best ResponseYou've already chosen the best response.0It's a with subscript (n+1) . I'm ask confused with your symbols

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Ah. So your new sequence is \(\{a_{n+1}\}\)?

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.0Hey, @kimmy0394 When you think about it \[\huge a_{n+1}\]is just the same sequence, just that it starts one step ahead of \[\huge a_n\] right?
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