Let f be a function with derivatives of all orders and for which f(2)=7. When n is odd, the nth derivative of f at x=2 is 0. When n is even and n=>2, the nth derivative of f at x=2 is given by f(n) (2)= (n-1)!/3n
a. Write the sixth-degree Taylor polynomial for f about x=2.
b. In the Taylor series for f about x=2, what is the coefficient of (x-2)(2n) for n =>1 ?
c. Find the interval of convergence of the Taylor series for f about x=2. Show the work that leads to your answer
The Attempt at a Solution
a. I got the sixth-degree series.
b. Will it just be (n-1)!/3n / (2n)! ??
c. So will the Taylor series be [tex]\sum[/tex] (n-1)/3n * (x-2)^2n from n=1 to infinity ??