Using the Taylor Series of expansion and finding the radius of convergence

How do I go about solving this?

Find the Taylor series for *f*(*x*) centered at the given value of *a*. [Assume that *f* has a power series expansion. Do not show that *R*(*x*) → 0.] *f*(*x*) = 6 cos *x*, *a* = 7*π*

*f*(*x*) =

Find the associated radius of convergence *R*.

*R* =

Re: Using the Taylor Series of expansion and finding the radius of convergence

Hint: 6cos(7π + x) = -6cos(x).

Re: Using the Taylor Series of expansion and finding the radius of convergence

Quote:

Originally Posted by

**emakarov** Hint: 6cos(7π + x) = -6cos(x).

Except that centring at $\displaystyle \displaystyle \begin{align*} a = 7\pi \end{align*}$ means you are expanding $\displaystyle \displaystyle \begin{align*} f(x - 7\pi) \end{align*}$, not $\displaystyle \displaystyle \begin{align*} f(x + 7\pi) \end{align*}$. Won't make any difference though :)