The discussion focuses on finding the Taylor Series for the function f(x) = 1/(1-6x) centered at c=6. The user initially attempts to derive the nth derivative and construct the series but misidentifies the function as f(x) = 1/(1-6). The correct nth derivative is expressed as (-6)^(n-1)n!/(1-6x)^(n+1), leading to the Taylor series representation of (-6)^(n-1)(x-6)^(n)/(1-6x)^(n+1). The discussion emphasizes the importance of starting from the definition of the Taylor series and suggests writing out the first few terms to identify patterns.
PREREQUISITESStudents studying calculus, particularly those focusing on series expansions, as well as educators looking for examples of Taylor Series derivation and application.
Did you mean: $$f(x) = \frac{1}{1-6x}$$ ... from below, it appears so.Soccerdude said:Homework Statement
Find the Taylor Series for f(x) = 1/(1-6) centered at c=6
What leads you to believe that?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
Start from the definition of the Taylor series.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?