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Interpret the given sum

  1. Dec 23, 2011 #1
    Interpret the given sum Sn as a sum of areas of rectangles approximating the area of a certain region in the plane, and hence evaluate (x→ infinity) lim Sn


    n
    Sn ∑2/n(1-((2i)/n))
    i=1

    http://s716.photobucket.com/albums/ww168/Pitoraq/?action=view&current=Rms2.jpg
    (number 17)

    Attempt at solution:

    I guess that the function is y = 1-2x is it right ?

    How to solve for lim when x →infinity ?
     
    Last edited: Dec 23, 2011
  2. jcsd
  3. Dec 23, 2011 #2

    HallsofIvy

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    Not quite. Notice that the [itex]\Delta x[/itex] is 2/n. And so "x" is 2i/n. Or, you could factor that 2 out of the sum so that [itex]\Delta x[/itex] is 1/n. In that case, "x" is indeed i/n. Do you see that those both give the same integral?
     
  4. Dec 23, 2011 #3

    Ray Vickson

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    x does NOTgo to infinity; n does. You could use standard algebraic formulas to evaluate the sum explicitly as a function of n, then let n go to infinity in that formula. You should have seen already all the summations you need, somewhere in your course notes or your textbook.

    RGV
     
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