Some rapidly converging series for zeta(2n+1)

For a natural number n, the author derives several families of series repre sentations for the Riemann Zeta function zeta(2n + 1). Each of these series representing zeta(2n + 1) converges remarkably rapidly with its general te rm having the order estimate: O(k(-2)n(-1).m(-2k))(k-->infinity; m = 2,3,4,6). Relevant connections of the results presented here with many other known se ries representations for zeta(2n + 1) are also pointed out.