A Note on a Sum of the Series 1/1.3 + 1/3.5 + 1/5.7 + ... = 1/2

Abstract

In this note it is shown that the interesting summation 1/1.3 + 1/3.5 + 1/5.7 + ... = 1/2 which was deduced from certain Fourier series, can be obtained very quickly with the help of classical Gauss hypergeometric summation theorem.