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Math Help - Limits, Monotonicity, and Bounding

  1. #1
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    Limits, Monotonicity, and Bounding

    I have attached the original problem statement.

    I'm not entirely sure how to show that the sequence is bounded. The book gave the hint of using the inequality ab<=1/2(a^2+b^2) to show xn+1>sqrt(a) for all n. I'm having trouble applying this inequality however, and am not really sure how to algebraically make use of it. I was looking at defining a and b for the variables, but what I am coming up with isn't making sense to me.

    Part b I can do

    Part c I was thinking of just working out algebraically by defining xn instead of xn-1 and changing the indexes. Does that sound like the right way to approach it.

    I mostly would like some help with part a)
    Attached Thumbnails Attached Thumbnails Limits, Monotonicity, and Bounding-scan0040.jpg  
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  2. #2
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    Smile Re: Limits, Monotonicity, and Bounding

    Quote Originally Posted by renolovexoxo View Post
    i have attached the original problem statement.

    I'm not entirely sure how to show that the sequence is bounded. The book gave the hint of using the inequality ab<=1/2(a^2+b^2) to show xn+1>sqrt(a) for all n. I'm having trouble applying this inequality however, and am not really sure how to algebraically make use of it. I was looking at defining a and b for the variables, but what i am coming up with isn't making sense to me.

    Part b i can do

    part c i was thinking of just working out algebraically by defining xn instead of xn-1 and changing the indexes. Does that sound like the right way to approach it.

    I mostly would like some help with part a)
    attached
    Attached Thumbnails Attached Thumbnails Limits, Monotonicity, and Bounding-001.jpg  
    Last edited by hedi; October 23rd 2012 at 02:03 PM. Reason: delete
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  3. #3
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    Re: Limits, Monotonicity, and Bounding

    attached
    Attached Thumbnails Attached Thumbnails Limits, Monotonicity, and Bounding-001.jpg  
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