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

• Jun 29th 2012, 04:32 AM
andvaka
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 = 7π

f(x) =

Find the associated radius of convergence R.
R =
• Jun 29th 2012, 04:53 AM
emakarov
Re: Using the Taylor Series of expansion and finding the radius of convergence
Hint: 6cos(7π + x) = -6cos(x).
• Jun 29th 2012, 05:16 AM
Prove It
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 \begin{align*} a = 7\pi \end{align*} means you are expanding \displaystyle \begin{align*} f(x - 7\pi) \end{align*}, not \displaystyle \begin{align*} f(x + 7\pi) \end{align*}. Won't make any difference though :)