Power Series Expansion for Real Arccosine Function

Theorem
The arccosine function has a Taylor Series expansion:


 * $\displaystyle \arccos x = \frac {\pi} 2 - \sum_{n \mathop = 0}^\infty \frac {\left({2n}\right)!} {2^{2n} \left({n!}\right)^2} \frac {x^{2n + 1}} {2n + 1}$

which converges for $-1 \le x \le 1$.

Proof
It follows from Taylor Series of Arcsine Function that the series is convergent for $-1 \le x \le 1$.