Menu Close

Prove-that-1-n-2-k-n-2-k-n-2-k-2-n-2-2n-1-n-1-




Question Number 31714 by gunawan last updated on 13/Mar/18
Prove that  Σ_1 ^(n−2) k ((( n−2)),((  k)) ) (((n+2)),((k+2)) ) = (n−2) (((2n−1)),((n−1)) )
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{\mathrm{1}} {\overset{{n}−\mathrm{2}} {\sum}}{k}\begin{pmatrix}{\:{n}−\mathrm{2}}\\{\:\:{k}}\end{pmatrix}\begin{pmatrix}{{n}+\mathrm{2}}\\{{k}+\mathrm{2}}\end{pmatrix}\:=\:\left({n}−\mathrm{2}\right)\begin{pmatrix}{\mathrm{2}{n}−\mathrm{1}}\\{{n}−\mathrm{1}}\end{pmatrix} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *