\sum\limits_{i \ge 2} {\frac{{x^{n + i - 2} }}{{i\left( {n + i - 2} \right)}}} = \frac{{1 - x^{n - 2} }}{{n - 2}}\ln \left( {1 - x} \right) + \frac{1}{{n - 2}}\sum\limits_{k = 1}^{n - 2} {\left( \begin{array}{c}
 n - 2 \\ 
 k \\ 
 \end{array} \right)\frac{{\left( {x - 1} \right)^k }}{k}} - \frac{{x^{n - 1} }}{{n - 1}}