Power Series Expansion for Real Area Hyperbolic Cosine

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

for $x \ge 1$.

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