  We derive exact closed-form expressions for several sums leading to
hyperbolic functions and discuss their applicability for studies of finite-size
Ising spin chains. We show how they immediately lead to closed-form expressions
for both fidelity susceptibility characterizing the quantum critical point and
the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick
adiabatic driving of the system. Our results generalize and extend the sums
presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and
Products.
