Power Series Expansion for Real Area Hyperbolic Cosine

Theorem
The (real) area hyperbolic cosine function has a Taylor series expansion:

for $x \ge 1$.

Lemma 1
We have that the (real) area hyperbolic cosine is defined for $x \ge 1$.

Let $z = \dfrac 1 x$.

Then we have:
 * $0 < \dfrac 1 z \le 1$

Now we consider:

Also see

 * Power Series Expansion for Real Area Hyperbolic Sine
 * Power Series Expansion for Real Area Hyperbolic Tangent
 * Power Series Expansion for Real Area Hyperbolic Cotangent
 * Power Series Expansion for Real Area Hyperbolic Secant
 * Power Series Expansion for Real Area Hyperbolic Cosecant