Taylor Series of f(x) = 1/(1-6x) at c=6

[Soccerdude]

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 n^th 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?

 

[Simon Bridge]

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 n^th 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.