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Sum of squares proof

  1. May 6, 2009 #1
    the proof in my text starts with whats called a telescoping sum (1+i^3)-i^3 what is the relevence of this to i^2
     
  2. jcsd
  3. May 6, 2009 #2
    a) Prove the formula for the partial geometric series:

    [tex]\sum_{k=0}^{n}x^{k}=\frac{1-x^{n+1}}{1-x}[/tex]


    Hint: Multiply both sides by 1-x.


    b) Substitute x = e^t in the formula for the partial geometric series.


    c) Perform a series expansion of both sides to second order in t.
     
  4. May 6, 2009 #3
    Shouldn't that be (1+i)^3 - i^3?

    If you expand (i+1)^3, you see that i^3 cancels and then you get a combinaton of the summaton of i^2 and i and of 1.
     
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