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Math Help - Series Problem

  1. #1
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    Series Problem

    Find ∑(x_i+i)^2 for i=5 to 168

    x_i represents the 'i'th value in the list of x values.


    I'm not really sure how to compute this. I'm worked with convergence tests and stuff for series, not familiar with solving this. More specifically, I don't understand what x_i represents in a way that I can plug it in and get a number for it.
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  2. #2
    Junior Member RaisinBread's Avatar
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    Re: Series Problem

    Just to clarify, your series is defined as;

    You have a sequence of real numbers, \{x_1,x_2,x_3,...\}, and you want to compute the sum
    \displaystyle \sum_{i=5}^{168} (x_i+i)^2

    Do you have any more information on your numbers x_n?
    Last edited by RaisinBread; November 23rd 2011 at 08:13 PM.
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  3. #3
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    Re: Series Problem

    Correct. And no, I'm afraid that's all that was provided. I am perplexed.
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  4. #4
    Junior Member RaisinBread's Avatar
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    Re: Series Problem

    Well, I guess what you could do is;

    \displaystyle \sum_{i=5}^{168} (x_i+i)^2 = \displaystyle \sum_{i=5}^{168} x_i^2 + 2i x_i + i^2 = \displaystyle \sum_{i=5}^{168} x_i^2 +2\sum_{i=5}^{168} i x_i +\sum_{i=5}^{168} i^2

    Here you can at least get \sum_{i=5}^{168} i^2 with the formula given at Square pyramidal number - Wikipedia, the free encyclopedia, use it for n=168 and the substract n=5. For the other two, nothing comes to my mind as of yet without any precisions on the sequence \{x_n\}.
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