<p>Express \(\mathrm{f}(x) = \frac{x^3 - x - 1}{(x^2 - 1)(x + 1)}\) in partial fractions. Hence find the series expansion of \(\mathrm{f}(x)\), in ascending powers of \(x\), up to and including the term in \(x^3\), simplifying your coefficients. </p>
<p>Find the coefficient of \(x^{2005}\).</p>

Express \(\mathrm{f}(x) = \frac{x^3 - x - 1}{(x^2 - 1)(x + 1)}\) in partial fractions. Hence find the series expansion of \(\mathrm{f}(x)\), in ascending powers of \(x\), up to and including the term in \(x^3\), simplifying your coefficients. 

Maclaurin Series and Power Series

International Baccalaureate Higher Level Mathematics