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Math Help - Limit Comparison Concept Help

  1. #1
    Junior Member
    Joined
    Jan 2010
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    25

    Limit Comparison Concept Help

    I need help understanding an informal principle when doing these equations.

    In my book it says that you can discard all but the leading terms. When can you do this?

    For example, one problem has sigma from 1 to infinity of (3k^3-2k^2+4)/(k^7-k^3+2)

    which can be compared to 3k^3/k^7 or 3/k^4 to check for covergence or divergence

    Why can't you get rid of the 3 in the numerator? Basically I don't understand how to use this rule. Can someone explain it in as simple terms as possible?
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  2. #2
    Senior Member
    Joined
    Jan 2010
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    You can get rid of the 3 in the numerator. A constant multiple won't affect the result.

    Comparing it to \frac{1}{k^4} is fine.

    Basically you are just taking the term that approaches infinity the "fastest" (in layman's terms). If it's a polynomial, then the term of the highest degree (exponent) is approaching infinity the "fastest", therefore we can disregard the other terms. We can do the same for the denominator.
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