Question

Find the power series for the following and determine the radius of convergence. f(x) = cos(x)
AWARD GIVEN AT END!

Answer 1

Assuming you want the general Taylor series about \(x=c\), that would be
\[f(x)=\sum_{n=0}^\infty \frac{(-1)^n}{(2n)!}(x-c)^{2n}\]

Answer 2

Okay so because its a power series its completely fine for me to use either Taylor or Maclaurin series?

Answer 3

Taylor series are power series, yes.

Answer 4

So this is correct? :)

Answer 5

@SithsAndGiggles ?

Answer 6

Yes, that's right.

Answer 7

To find the radius of convergence, use the ratio test.

Answer 8

Sooo its 0?

Answer 9

@SithsAndGiggles :)