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Math Help - Limit

  1. #1
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    Limit

    compute the lim as n approaches infinity (1/3n + 1/(3n + 1) + 1/(3n + 2) + ...+ 1/(4n -1))
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Susie38
    compute the lim as n approaches infinity (1/3n + 1/(3n + 1) + 1/(3n + 2) + ...+ 1/(4n -1))
    Let:

    <br />
S_n=\frac{1}{3n}+\frac{1}{3n+1}+\dots+\frac{1}{4n-1}<br />

    Now (you will need to justify this, but its a standard trick):

    <br />
\int_{3n}^{4n} \frac{1}{x-1}\ dx>S_n>\int_{3n}^{4n} \frac{1}{x}\ dx<br />

    Which will be sufficient to show that:

    \lim_{n \to \infty} S_n=\log(4/3)

    RonL

    (A partial explanation of how the "trick" works can be found here ).
    Last edited by CaptainBlack; June 6th 2006 at 11:07 PM. Reason: inequalities the wrong way around
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  3. #3
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    my professor said for a hint multiply each term by n/n. how does this help?
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