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Proof for Newton's Sums

  1. Aug 6, 2008 #1
    Could anyone provide me with a proof for Newton's Sums?

    So far, I've gotten as far as showing for a polynomial P(x)=anxn+an-1xn-1+...+a1x+a0 with roots x1, x2,..., xn that


    and so,




    but I don't know if I'm heading in the right direction and I can't seem to go anywhere that seems to lead towards Newton's sums. Any suggestions will be much appreciated. Thanks.
  2. jcsd
  3. Aug 6, 2008 #2


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    What are Sn, Sn-1, Supn+ k, etc.?
  4. Aug 6, 2008 #3


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    ForMyThunder: http://www.mathlinks.ro/viewtopic.php?t=213867

    HoI: http://www.artofproblemsolving.com/Wiki/index.php/Newton_sums [Broken]
    Last edited by a moderator: Apr 23, 2017 at 2:46 PM
  5. Aug 6, 2008 #4
    Sm = x1m+x2m+x3m+...xn-1m+xnm
  6. Aug 6, 2008 #5
    Oh, thanks. :)
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