The limit of the Riemann zeta function and its nontrivial zeros

Abstract

In this article, with a new approach, which is not discussed in the literature yet, the limit of the Riemann zeta function or Euler-Riemann zeta function is approximately explored by applying Dirichlet's rearrangement theorem for absolutely convergent series to the Riemann zeta function by rearranging its terms as geometric series for sufficiently large $n$. The limit of the Riemann zeta function or Euler-Riemann zeta functions, $\lim_{n\to\infty} \zeta(z)$, is first time explored. The limit obtained here is a very promising for the nontrivial or complex zeros of the Rieman zeta function.