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## Homework Statement

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)!/3

^{n}

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

## Homework Equations

Taylor series

## The Attempt at a Solution

a. I got the sixth-degree series.

b. Will it just be (n-1)!/3

^{n}/ (2n)! ??

c. So will the Taylor series be [tex]\sum[/tex] (n-1)/3

^{n}* (x-2)^2n from n=1 to infinity ??