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Simplify-n-1-C-2-2-n-2-C-2-3-n-3-C-2-n-2-2-C-2-




Question Number 22389 by Tinkutara last updated on 17/Oct/17
Simplify:  ^(n−1) C_2 +2^(n−2) C_2 +3^(n−3) C_2 +...+(n−2)^2 C_2
$${Simplify}: \\ $$$$\:^{{n}−\mathrm{1}} {C}_{\mathrm{2}} +\mathrm{2}\:^{{n}−\mathrm{2}} {C}_{\mathrm{2}} +\mathrm{3}\:^{{n}−\mathrm{3}} {C}_{\mathrm{2}} +…+\left({n}−\mathrm{2}\right)\:^{\mathrm{2}} {C}_{\mathrm{2}} \\ $$

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