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Finding a taylor series

  1. Nov 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Find a taylor series for f(x)=sq. rt. of X about c=1


    2. Relevant equations
    N/A


    3. The attempt at a solution
    I took the derivative of the sq rt of X, and then plugged in 1 for all the X's. I got:
    f(x)= 1
    f'(x)=1/2
    f''(x)=-1/4
    f'''(x)=3/8
    f^4(x)=-15/16

    My teacher said it's okay to take out the first 2 terms because I can't seem to find a pattern that includes them, so I have so far:

    1+1/2(x-1) + Sigma where n=1 to infinity, of (-1)^n(x-1)^n/n!

    The denominators seem to fit the pattern 2^n, and I've found the numerator to be (2n-1)!!

    Can anyone find a pattern that doesnt use a double factorial? I've never used double factorials before, so I'm not even sure I'm using them correctly.

    Thank you!
     
  2. jcsd
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