  In this paper, by introducing a new operation in the vector space of Laurent
series, the author derived explicit series for the values of $\zeta$-funtion at
positive integers, where $\zeta$ denotes the Riemann zeta function. The values
of $\zeta(k),\ k>1$ are largely connected with Bernoulli numbers and binomial
numbers. The method in this paper seems new, and the resluts are about
divergent series. Using Borel summation for these divergent series one can
connect $\zeta$ function, Bernoulli numbers, and most series representations of
Riemann zeta function.
