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Published online by Cambridge University Press: 17 April 2009
Let N be a fixed positive integer. In this paper, we apply a newly developed method of Eie and Lai to the evaluation of certain infinite trigonometric series. Indeed, we are able to express the sums of these series in terms of Bernoulli polynomials. That is, we obtain several new Bernoulli identities. A similar method leads to Ramanujan's identities.