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Power Series for sqrt(x+1)

  1. Dec 18, 2009 #1
    How would you go about finding the power series for sqrt(x+1) by applying the square root algorithm. I can do it using binomial expansion and other formulas but I'm not familiar with the square root algorithm involving variables.
     
  2. jcsd
  3. Dec 18, 2009 #2

    HallsofIvy

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    Which square root algorithm do you mean? There are several.
     
  4. Dec 20, 2009 #3
    [tex]\int\sqrt{x+1}\rightarrow \frac{2}{3}(x+1)^{\frac{1}{2}}[/tex]

    It's just the usual 1/n+1x^n+1.

    and nx^n-1

    [itex]\frac{d}{dx} \sqrt {x+1} \rightarrow \frac{1}{2(x+1)^\frac{1}{2}}[/itex]

    Which you can expand to a series using the inequality:

    [itex](2x + r) r\leq a - x^2[/itex]
     
    Last edited: Dec 20, 2009
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