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Still Stuck on Binomial series

  1. Apr 3, 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)] =

    The coefficients of the binomial series are:
    '1/2 choose 0' is 1.
    '1/2 choose 1' is 1(1/2)/1 = 1/2
    '1/2 choose 2' is 1/2(1/2-1)/2 = -1/8
    '1/2 choose 3' is -1/8(1/2-2)/3 = 1/16
    '1/2 choose 4' is 1/16(1/2-3)/4 = -5/128

    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]

    = 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 3, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    An even power of a negative number is POSITIVE. Check the signs again. ALL signs come out overall negative. Except '1', of course.
     
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