A typical problem in physics is that physical quantities can be calculated for a series of finite systems, but ultimately, we would like to know the results for the infinite system. Hulthen (1938) studied the one-dimensional Spin Heisenberg model with the Hamiltonian
where is the spin at the site and is the total number of sites in the system. From the eigen equation
Hulthen obtained the ground-state energy per site, for a series of finite systems with
Now assume that the ground-state energy per site is given by
Truncate the above series at and find by solving the linear equation set numerically.