Inductive construction of rapidly convergent series representations for ζ(2n+1)

For a natural number n. the authors, propose and develop a method of inductive construction of several (presumably new) rapidly convergent series representations for the values of the Riemann Zeta function (2n + 1). Under a certain assumption, the various series representations for (2n + 1), which are derived here by using this method. converge remarkably rapidly with their general terms having the order estimate: O(k(-2n-m).2(-2k)) (k --> infinity), where in is an arbitrary natural number. Numerical and symbolic computational aspects of some of the results presented here are also considered.