  Using the fact that a finite sum of power series are given by the difference
between two zeta functions, we justify the usage of the zeta function with a
negative variable in physical problems to avoid the divergence of the infinite
sum. We will show that in the case of magnetization of graphene, the zeta
function with negative variable arises as a result of cut-off energy between
two consecutive Landau levels. Furthermore, similar justification can be
applied to the case of zero temperature Casimir force in parallel-plate
geometry.
