- 求和\[
\sum_{k=0}^n k {n \choose k}
\]
解法：\[
\begin{align}
(x = 1 时)\sum_{k=0}^n k {n \choose k} & = \sum_{k=0}^n {n \choose k}\frac{\partial}{\partial x} x^k = \frac{\partial}{\partial x} \sum_{k=0}^n {n \choose k} x^k = n(x+1)^{n-1} = n 2^{n-1}
\end{align}
\]
- 求和\[
\sum_{k=0}^n k^2 {n \choose k}
\]
解法：\[
\begin{align}
(x = 1 时)\sum_{k=0}^n k^2 {n \choose k} & = \sum_{k=0}^n {n \choose k}\frac{\partial}{\partial x} x \frac{\partial}{\partial x} x^k = \frac{\partial}{\partial x} x \frac{\partial}{\partial x} \sum_{k=0}^n {n \choose k} x^k = ……
\end{align}
\]
完本（整理）
原文：https://www.cnblogs.com/buzhiyusheng/p/11946092.html
