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kimmy0394

  • 3 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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  1. KingGeorge
    • 3 years ago
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    Since it converges, you have that for all \(\epsilon>0\), \(|L-a_n|<\epsilon\) 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?

  2. kimmy0394
    • 3 years ago
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    It's a with subscript (n+1) . I'm ask confused with your symbols

  3. KingGeorge
    • 3 years ago
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    Ah. So your new sequence is \(\{a_{n+1}\}\)?

  4. kimmy0394
    • 3 years ago
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    Yes

  5. terenzreignz
    • 3 years ago
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    Hey, @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?

  6. kimmy0394
    • 3 years ago
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    right!

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