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Summation problem

  1. Oct 20, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]\Sigma^{4}_{k=0}[/tex] [tex]\stackrel{1}{k^{2}+1}[/tex]

    2. Relevant equations

    I would imagine it has something to do with this property

    [tex]\Sigma^{n}_{i=1}[/tex] [tex]i^{2}[/tex] = [tex]\stackrel{n(n+1)(2n+1)}{6}[/tex]

    3. The attempt at a solution

    So at first I thought I could bring [tex]k^{2}[/tex]+1 to the top by,


    However that didn't work.

    I do know that I can solve it by

    [tex]\stackrel{1}{0^{2}+1}[/tex]+[tex]\stackrel{1}{1^{2}+1}[/tex] and so on and so for so forth but I want to know how to apply the properties.
    Last edited: Oct 20, 2008
  2. jcsd
  3. Oct 20, 2008 #2
    sorry I suppose the computer doen't like my problem...I thought i put it in right. If it helps I'll write it out. the problem is,

    Sigma with the upper bound being 4 and the lower bound being 0 and the function is one divided by (k squared plus 1)

    Hopefully the rest can be figured out...just think of it as a puzzle, lol.
  4. Oct 20, 2008 #3


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    So the problem is to add 1/(k2+ 1) for k= 0 to 4? That's just an arithmetic problem!

    1/1+ 1/(4+1)+ 1/(9+1)+ 1/(16+1)= what?
  5. Oct 20, 2008 #4
    yes but I wanted to see how this may apply to the formula [n(n+1)(2n+1)]/6 for any k squared or maybe a different formula I'm not aware of because what if the problem went form 0-150 there is no way anyone would want to work that out the way you did.
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