Convergence Theorems for Series of Positive Terms

This paper brings together certain theorems which enable 00 us to settle the convergence or divergence of Σ a_n, (a_n > 0) with the help of a suitably chosen integral ∫ F(x) dx, F(x) > 0. The theorems include as particular cases all the convergence criteria, in common use, for series of positive terms, and suggest a simple and not inelegant method of presenting such criteria within the framework of a single idea.