Menu Close

Category: Permutation and Combination

Question-163263

Question Number 163263 by Ar Brandon last updated on 05/Jan/22 Answered by qaz last updated on 05/Jan/22 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{k}} \mathrm{k}(nk)=\frac{\partial}{\partial\mathrm{x}}\mid_{\mathrm{x}=\mathrm{1}} \left(\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}(nk)\left(−\mathrm{x}\right)^{\mathrm{k}} −\mathrm{1}\right)=\frac{\partial}{\partial\mathrm{x}}\mid_{\mathrm{x}=\mathrm{1}}…