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Math Help - sequence limit and convergence

  1. #1
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    sequence limit and convergence

    have been given sequence

    bn = 2n-9/(10(0.5)^n)+2

    i trying to find if it converges or not and the limit.
    any ideas would be welcomed.
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  2. #2
    MHF Contributor
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    Hi

    Could you rewrite with parentheses so that we can understand which are the numerator and the denominator ?
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  3. #3
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    2n-9 numerator
    10(0.5)^n +2 denominator

    we have 10(0.5)^n plus 2 and not n+2 as power

    hope this helps
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  4. #4
    MHF Contributor
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    OK so b_n = \frac{2n-9}{10(0.5)^n+2}

    What is the limit of the numerator ? What is the limit of the denominator ?
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  5. #5
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    for denominator as n gets larger (0.5)^n will converge to 0 so limit will be 2
    but 2n-9 will increase as n gets larger not sure what happen guess it will not be convergent.

    i am guessing the sequence will behave like-9/2 mulitiply by 2n which is not convergent ?
    Last edited by mr fantastic; April 27th 2009 at 03:06 AM. Reason: Merged posts
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