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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

    P(x1)+P(x2)+P(x3)+...+P(xn)=0

    and so,

    anSn+an-1Sn-1+...+a1S1+na0=0

    and,

    anSn+k+an-1Sn+k-1+...+a1Sk+1+a0Sk=0

    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

    HallsofIvy

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

    benorin

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  5. Aug 6, 2008 #4
    Sm = x1m+x2m+x3m+...xn-1m+xnm
     
  6. Aug 6, 2008 #5
    Oh, thanks. :)
     
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