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We study an elementary series that can be considered a relative of a seriesstudied by Ramanujan in Part 1 of his Lost Notebooks. We derive a closed formfor this series in terms of the inverse hyperbolic arctangent and thepolylogarithm. Special cases will follow in terms of the Riemann zeta and thealternating Riemann zeta function. In addition, some trigonometric series willbe expressed in terms of the Clausen functions. Finally, a range of newtwo-term dilogarithm identities will be proved and some difficult seriesinvolving Lucas numbers will be evaluated in closed form.

A series of Ramanujan, two-term dilogarithm identities and some Lucas series