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Math Help - Algebra of limits property proof

  1. #1
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    Algebra of limits property proof

    Let (a_n) be a convergent sequence with limit L and let k be a natural number. Show that (a_n+k) is also convergent with limit L.

    Any help would be greatly appreciated
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Algebra of limits property proof

    limit L or limit L + K ?
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  3. #3
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    Re: Algebra of limits property proof

    Quote Originally Posted by sakuraxkisu View Post
    Let (a_n) be a convergent sequence with limit L and let k be a natural number. Show that (a_n+k) is also convergent with limit L.
    I am sure that he/she means (s_{n+k}).
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  4. #4
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    Re: Algebra of limits property proof

    The sequence converges to L means that, given any \epsilon> 0 there exist an integer N such that if n> N, |a_n- L|< \epsilon. For the sequence a_{n+k} just shift N to N+k
    Thanks from sakuraxkisu
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