I am working in the following series i get a result could you help to see the convergence any ideas $$\sum _{k=1}^{\infty } \frac{(-1)^{k+1} \text{Li}_k(-a)}{a}=\frac{a-\log (a+1)}{a^2}$$ where Lk is the polylogaritm.
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Have you tried writing the polylogarithm as an integral, and then switching the order of summation and integration? – Lucian Oct 02 '14 at 13:58
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Yes lucian you are wright but o do not show the convergence of the serie – Oct 02 '14 at 17:24