(解決済)なんですか、これは？

187

$W \in R, W > 0, n \in N, n > 1$ :

$\begin{array}{rcl} \overset{―}{W_{1}} & = & \frac{1}{W} \int_{0}^{W} w_{1} d w_{1} \\ \overset{―}{W_{2}} & = & \frac{1}{W} \int_{0}^{W} \frac{1}{W - w_{1}} \int_{0}^{W - w_{1}} w_{2} d w_{2} d w_{1} \\ \overset{―}{W_{3}} & = & \frac{1}{W} \int_{0}^{W} \frac{1}{W - w_{1}} \int_{0}^{W - w_{1}} \frac{1}{W - w_{1} - w_{2}} \int_{0}^{W - w_{1} - w_{2}} w_{3} d w_{3} d w_{2} d w_{1} \\ \overset{―}{W_{4}} & = & \frac{1}{W} \int_{0}^{W} \frac{1}{W - w_{1}} \int_{0}^{W - w_{1}} \frac{1}{W - w_{1} - w_{2}} \int_{0}^{W - w_{1} - w_{2}} \frac{1}{W - w_{1} - w_{2} - w_{3}} \int_{0}^{W - w_{1} - w_{2} - w_{3}} w_{4} d w_{4} d w_{3} d w_{2} d w_{1} \\ \overset{―}{W_{n}} & = & \frac{1}{W} \int_{0}^{W} \frac{1}{W - w_{1}} \int_{0}^{W - w_{1}} \frac{1}{W - w_{1} - w_{2}} \int_{0}^{W - w_{1} - w_{2}} \dots w_{n} d w_{n} \dots d w_{3} d w_{2} d w_{1} \end{array}$