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Stuck on Binomial Series

  1. Apr 2, 2008 #1
    Use binomial series to approximate sqrt (35) with an accuracy of 10^(-7)

    (35) = sqrt(35*36/36) = 6*sqrt(35/36)
    Formula: (1+x)^n where x=(-1/36) and n=(1/2):

    6*sqrt(35/36) = 6[(1 + (- 1/36))^(1/2)] =

    from k=0 to k=4:
    = 6[(1 - (1/2)*(1/36) + (1/8)*(1/36)^2 - (1/16)*(1/36)^3 +
    (5/128)*(1/36)^4]

    = 5.917237472 but it has to be more accurate

    I don't know where the mistake is in the series. I used the 4 terms because (5/128)(1/36) = 2.30*10^(-8) Please help, thanks again.
     
  2. jcsd
  3. Apr 2, 2008 #2

    mathman

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    Science Advisor
    Gold Member

    The coefficient for the square term should be -1/8, not 1/8. Specifically it is (1/2)(-1/2)/2.

    I didn't look any further.
     
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