Prove (binomial)

M

metru

New member
Joined
Jul 22, 2005
Messages
3
Prove:
Ck−3k−3⋅Cn−k+22+Ck−2k−3⋅Cn−k+12+Ck−1k−3⋅Cn−k2+⋯+Cn−3k−3⋅C22=Cnk\displaystyle C_{k - 3}^{k - 3} \cdot C_{n - k + 2}^2 + C_{k - 2}^{k - 3} \cdot C_{n - k + 1}^2 + C_{k - 1}^{k - 3} \cdot C_{n - k}^2 + \cdots + C_{n - 3}^{k - 3} \cdot C_2^2 = C_n^k
 
I proved it using a napkin at Burger King; sorry, lost the napkin :roll:
 
You must log in or register to reply here.
Top