  We utilize undetermined coefficient method and an iterative method to
construct the series solutions of the 3D Cauchy problem for a class of
incompressible Navier-Stokes and Euler Equations. Then we can turn the
Navier-Stokes Equations (Euler Equations) into the Cauchy problem for finitely
(infinitely) many ordinary differential equations. We get the finite series
solution of the Navier-Stokes Equations. By using some combinatorial identities
techniques, we prove that the sum of the solutions to these ordinary
differential equations is an infinite series solution of the Euler Equations in
some cases.
