C0CR +C1CR+1 +C2CR+2....+CN-RCN= 2N!/(N-R)!(N+R)! PROVE..

C0CR +C1CR+1  +C2CR+2....+CN-RCN= 2N!/(N-R)!(N+R)!







1 Answers

iit hub
16 Points
9 years ago

this can be written as C0Cn-r + C1Cn-r-1 + C2Cn-r-2 +..........+ Cn-rC0

to get this sum you can consider (1+x)n(x+1)

when you expand the two and multiply the terms you will find that the coefficient of xn-r is the required sum.

Hence to get the sum you only need to find the coefficient of xn-r in  (1+x)n(x+1)n  i.e. (1+x)2n i.e 2nCn-r

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