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In this paper we provide a new series representation for the values ofRiemann zeta function at integer arguments, namely: $\zeta(m)=\sum_{n=1}^{\infty}\frac{m(-1)^{n-1}\Gamma(1-\omega_{m}n)...\Gamma(1-\omega_{m}^{m-1}n)}{n!n^m}$,where $n$ is an integer that lager than $1$ and $\omega$ is the $m$-th root ofunity. This series converges quite fast. It's derived by some technique ofinfinite partial fraction decomposition. With this technique we also establishother useful formulas related to gamma function.

A New Series Representation Involving Root Of Unity For The Values Of Riemann Zeta Function At Integer Arguments