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In this paper we discuss the important Abel's summation formula, which is a very powerful tool for analysing series of real or complex numbers. We derive from it an integral test which may be useful in cases where the classical integral test may not be applied. We also discuss how this new integral test may be used when one is dealing with alternating series of real or complex numbers. The main goal of this note is to provide a supplementary material for courses dealing with infinite series of real or complex numbers. [ABSTRACT FROM AUTHOR]

We use freshman calculus to prove thatfor θ ∈ (0, π) andn= 0, 1, 2, … ; in particular, we obtain a simple unified method for evaluating the following infinite series: [ABSTRACT FROM PUBLISHER]

A class of infinite series is evaluated with the aid of Taylor's theorem and a comparison is made with other methods. [ABSTRACT FROM AUTHOR]