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Thread: Prove this limit

  1. #1
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    Prove this limit

    Hello, can anyone give any hint regarding this? I'm lost.

    Prove that if Lim an = p
    n-->infinity
    then,
    Lim ( a1 + a2+ .......an )/n = p
    n-->infinity

    Can't get started.
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  2. #2
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    hey, can we use supremum and infemum concept here?
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  3. #3
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    Quote Originally Posted by concern View Post
    Hello, can anyone give any hint regarding this? I'm lost.

    Prove that if Lim an = p
    n-->infinity
    then,
    Lim ( a1 + a2+ .......an )/n = p
    n-->infinity

    Can't get started.
    Replacing a_n by b_n = a_n - p (for all n), you reduce the problem to the case where p=0. The proof for that case is given in this thread.
    Thanks from topsquark
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  4. #4
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    Re: Prove this limit

    I actually have to solve this same problem, and I clicked on "this thread" but it just brought me to the general page of all the threads. I've been trying to find it but I'm not getting anywhere, is there a more specific location I can find the thread that solves this problem? Please help!!
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  5. #5
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    Re: Prove this limit

    As the link to my previous solution to this problem no longer seems to work, I have posted a response to this thread at

    \text{http://www.mathhelpb}\hspace{0.01pt}\text{oards.com/f52}
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