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