Answer
Centred at $\pi$.
Work Step by Step
Re-write the given series in the expanded form as follows:
$\Sigma_{n=0}^\infty \dfrac{(-1)^n(x-\pi)^{2n}}{2n!}=\dfrac{(x-\pi)^0}{(2)(0!)}+\dfrac{-(x-\pi)^2}{2!}+\dfrac{(x-\pi)^4}{4!}+.....$
We can see that the above power series is centred at $\pi$.
