Question

I don't know how to write the combinatorial proof for this problem. If anyone could help me out that would be much appreciated.

1 (2n) (1 point n+1 n 2n-1 8. Show that for all n ,1-n)(1 point)

Answer 1

Given (2n- 1 n) - (2n - 1 n - 2) (2n - 1 n) - (2n - 1 n - 2) = (2n -1 1)!/n!(n - 1)! - (2n - 1)!/(n - 2)! (n + 1) = (2n - 1)!/(n - 2)! n!(1/n - 1 - 1/n + 1) = (2n - 1)!/n!(n - 2)!(2/(n - 1)(n + 1)) = 2(2n - 1)!/(n + 1)(n - 1)! n! = 1/n + 1(2n n) Hence (2n - 1 n)- (2n - 1 n - 2) = 1/n + 1(2n n)