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Math Help - Series

  1. #1
    Junior Member hoeltgman's Avatar
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    Series

    Consider the serie:
     u(n) := \dfrac{E(10^nx)}{10^n}
    E(x) means the integer part of x (E(5.2) = 5 for example)

    The limit of the serie is x.

    Now suppose x < x' and show that u(n) < u'(n).

    u(n) is the serie of x and u'(n) the serie of x'.

    I actually found a way, but it's not really good, because it contains a small contradiction. I wondered whether somebody knows who to get around that contradiction.

    This is what I got when I started with the definitions of a serie:

    x-x' < u(n) - u'(n) < x-x'

    If I ignore the left part it works, but the way it stands there now, it's impossible since a number cannot be strictly smaller than itself.
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  2. #2
    Super Member Rebesques's Avatar
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    Now suppose x < x' and show that u(n) < u'(n).
    Since x<x', we have E(10^n*x)<E(10^n*x'), divide by 10^n and we are done. Or have I misunderstood?
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  3. #3
    Junior Member hoeltgman's Avatar
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    God how stupid and I didn't get it!!!!! It's correct. I just have to add that it this is true for n large enough. (If n=1 and you take 5.2 and 5.27 it doesn't work. You have to assume that n > 2 then. for example) But that's it! Thx a 1000 times!!!
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