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Sum of function inside radicals

  1. Oct 24, 2012 #1
    Hi,

    Is there a general algebraic expression for the sum of a function inside a radical? I mean for something like this?

    [itex]\sum^{n}_{i=1}\sqrt{f(i)}[/itex]

    The specific case is given with constant c:

    [itex]\sum^{n}_{i=1}\sqrt{c^4i^4+c^2i^2+1}[/itex]

    And I supposed a related question is that, is there some way of extracting out just the radical as a separate sum of sqrt(i) or something which will leave three relatively simpler sums below?

    [itex]\sum^{n}_{i=1}c^4i^4+\sum^{n}_{i=1}c^2i^2+\sum^{n}_{i=1}1[/itex]
    [itex]=c^4\sum^{n}_{i=1}i^4+c^2\sum^{n}_{i=1}i^2+\sum^{n}_{i=1}1[/itex]

    Thanks!
     
  2. jcsd
  3. Oct 24, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, that cannot be simplified.
     
  4. Oct 24, 2012 #3
    :(

    Is there any chance a novice could perhaps determine a pattern to the series given enough time and energy? Or is there some strong mathematical reason why it simply isn't possible?
     
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