# Thread: sum of combinations

1. ## sum of combinations

Hello ,
I need help to prove that :
(2n)! / (n! * n!) + (2n-1)! / ( (n-1)! * n! ) + (2n-2)! / ( (n-2)! * n! ) + ... + n!/( 0! * n!) = (2n+1)! / ( n! * (n+1)! )

or C2nn + C2n-1n + ... + Cnn =C2n+1n+1

I applied mathematical induction and it didn't work or i did something wrong.
I appreciate your help !

2. ## Re: sum of combinations

You need to generalize the statement you are proving. Show $C_m^n+C_{m-1}^n+\dots+C_n^n = C_{m+1}^{n+1}$ by induction on m.

3. ## Re: sum of combinations

Thank you emakarov , i successfully applied mathematical induction on m .
You really saved me . Thanks.