Use Sequences to improve the numerical Riemann method to calculate integrals

Abstract The purpose of this research is the improvement of the numerical Riemann's integral using series. Riemann's method displayed in this research and we suggested an algorithm to improve the convergence using Geometric series, p-series and Taylor series for the exponential function. And we ended the discussion for this method by use some examples and we noticed that the Geometric series is the best series to get the nearby numerical solution from exact solution.