Taylor Series

  • Thread starter Soccerdude
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  • #1

Homework Statement



Find the Taylor Series for f(x) = 1/(1-6) centered at c=6

Homework Equations




Ʃ Fn(a)(x-a)/n!
n=0

The Attempt at a Solution



I believe that the nth derivative of 1/(1-6x) is

(-6)n-1n!/(1-6x)n+1

So i figured that the taylor series at c=6 would be

(-6)n-1(x-6)n/(1-6x)n+1

What am I doing wrong here?
 

Answers and Replies

  • #2
Simon Bridge
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Homework Helper
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Homework Statement



Find the Taylor Series for f(x) = 1/(1-6) centered at c=6
Did you mean: $$f(x) = \frac{1}{1-6x}$$ ... from below, it appears so.

Homework Equations




Ʃ Fn(a)(x-a)/n!
n=0

The Attempt at a Solution



I believe that the nth derivative of 1/(1-6x) is

(-6)n-1n!/(1-6x)n+1
What leads you to believe that?
So i figured that the taylor series at c=6 would be

(-6)n-1(x-6)n/(1-6x)n+1

What am I doing wrong here?
Start from the definition of the Taylor series.
Try writing out the 1st 3-4 terms and see if you spot a pattern.
 

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