Ononot — The dilogarithm function is defined as \operatorname{Li}2(x)

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Infinite Serieshard

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The dilogarithm function is defined as $\operatorname{Li}_2(x) = \sum_{n=1}^{\infty} \frac{x^n}{n^2}$ . Using the identity $\operatorname{Li}_2(x) + \operatorname{Li}_2(1-x) = \frac{\pi^2}{6} - \ln(x)\ln(1-x)$ for $x \in (0, 1)$ , evaluate the series $\sum_{n=1}^{\infty} \frac{1}{n^2 2^n}$ .