rt,设 Tn,k={kn}n!n−kT_{n,k}= \begin{Bmatrix} k \\ n \end{Bmatrix}n! n^{-k}Tn,k={kn}n!n−k 求 ∑k=n∞k×(Tn,k−Tn,k−1)\sum_{k=n}^\infty k\times(T_{n,k}-T_{n,k-1})∑k=n∞k×(Tn,k−Tn,k−1) 收敛性还都不清楚,不过 mma 没说不收敛(