By expanding (x/(1 - x))^n , 0<x<1 , in 2 ways, prove that:
nC0(2n-1)Cn - nC1(2n - 2)Cn + nC2(2n - 3)Cn - ... = 1
NOTE: nC0 represents n choose 0.
nC0(2n-1)Cn represents (n choose 0) multiplied by (2n - 1 choose n)
By expanding (x/(1 - x))^n , 0<x<1 , in 2 ways, prove that:
nC0(2n-1)Cn - nC1(2n - 2)Cn + nC2(2n - 3)Cn - ... = 1
NOTE: nC0 represents n choose 0.
nC0(2n-1)Cn represents (n choose 0) multiplied by (2n - 1 choose n)