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Convergence Theorems for Series of Positive Terms


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1 Christian College, Madras, India
     

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This paper brings together certain theorems which enable 00 us to settle the convergence or divergence of Σ an, (an > 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.
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  • Convergence Theorems for Series of Positive Terms

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Authors

C. T. Rajagopal
Christian College, Madras, India

Abstract


This paper brings together certain theorems which enable 00 us to settle the convergence or divergence of Σ an, (an > 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.