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Question Number 31714 by gunawan last updated on 13/Mar/18 | ||
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\mathrm{1}} {\overset{{n}−\mathrm{2}} {\sum}}{k}\begin{pmatrix}{\:{n}−\mathrm{2}}\\{\:\:{k}}\end{pmatrix}\begin{pmatrix}{{n}+\mathrm{2}}\\{{k}+\mathrm{2}}\end{pmatrix}\:=\:\left({n}−\mathrm{2}\right)\begin{pmatrix}{\mathrm{2}{n}−\mathrm{1}}\\{{n}−\mathrm{1}}\end{pmatrix} \\ $$ | ||