Finding a taylor series

  • #1

Homework Statement


Find a taylor series for f(x)=sq. rt. of X about c=1


Homework Equations


N/A


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!
 

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