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Calculus and Beyond Homework Help
Finding a taylor series
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[QUOTE="Calcgeek123, post: 2464899, member: 200973"] [h2]Homework Statement [/h2] Find a taylor series for f(x)=sq. rt. of X about c=1 [h2]Homework Equations[/h2] N/A [h2]The Attempt at a Solution[/h2] 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 doesn't use a double factorial? I've never used double factorials before, so I'm not even sure I'm using them correctly. Thank you! [/QUOTE]
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Finding a taylor series
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