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Math Help - Stuck on Sigma Notation Problem

  1. #1
    Newbie Rker's Avatar
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    Stuck on Sigma Notation Problem

    Hi guys. I've been viewing your website for a while now for guidance, but I haven't been able to solve this problem. Thus, I've registered to ask this question.

    I've been putting off this homework until the end of spring break, and now I totally forgot how to do it. If anyone here knows how to do this problem, it'd be immensely appreciated if you could show me the steps to solve it.



    Thank you!
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  2. #2
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    Quote Originally Posted by Rker View Post
    Hi guys. I've been viewing your website for a while now for guidance, but I haven't been able to solve this problem. Thus, I've registered to ask this question.

    I've been putting off this homework until the end of spring break, and now I totally forgot how to do it. If anyone here knows how to do this problem, it'd be immensely appreciated if you could show me the steps to solve it.



    Thank you!
    Part 1:

    Note that  \sum_{i=1}^n \left( 1 + \frac{2i}{n} \right) \left( \frac{2}{n}\right) = \frac{2}{n} \sum_{i=1}^n 1 + \left(\frac{2}{n}\right)^2 \sum_{i=1}^n i.

    \sum_{i=1}^n i = \frac{n (n+1)}{2} and \sum_{i=1}^n 1 = n.

    Substitute, simplify and then take the limit.
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  3. #3
    Math Engineering Student
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    Dunno if you've covered Riemann sums but you can turn that one into an integral.
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  4. #4
    Flow Master
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    Quote Originally Posted by Krizalid View Post
    Dunno if you've covered Riemann sums but you can turn that one into an integral.
    I suspect (looking ahead to part 2) that the OP has to evaluate the integral using the Riemann sum rather than evaluate the Riemann sum using an integral. Of course, correctly evaluating the integral provides a check that the Riemann sum has been calculated correctly ....
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